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Sekulovic, S. Segmentation of the Market of Consumer Goods by the Function of the Strength of Preference for One Brand over the Other, Year: 1983

Economic Analysis and Workers's Management 17()4. Editor: Branko Horvat. Indexed in: Journal of Economic Literature. YU ISSN 0013-3213.

Sekulovic, S. The Complete or Total Coefficient of Aggregate Demand Elasticity, Year: 1989

Economic Analysis and Worker's Management, 23()2. Editor: Branko Horvat. Indexed in: Journal of Economic Literature. YU ISSN 0351-286 X

This paper brings out the concept of the Average Base Index (ABI), an economic indicator that synthesizes in itself the simultaneous price movements of a set of homogeneous and brand name goods/services on a pencil of straight lines, in real Euclidean space ${E}^{n}$. Follows the construction of the Complete or Total Coefficient of Aggregate Demand Elasticity on a pencil of straight lines in ${E}^{n}$ and its interpretations.

Sekulovic, S. The Generalization of the Complete or Total Coefficient of Aggregate Demand Elasticity, Year: 1990

Economic Analysis and Worker's Management, 24()4. Editor: Branko Horvat. Indexed in: Journal of Economic Literature. YU ISSN 0351-286 X

This research introduces the Average Chain Index (ACI), an economic indicator which incorporates the simultaneous price movements of a set of homogeneous and brand name goods on a polygonal line, in real Euclidean space ${E}^{n}$. Also, the Complete or Total Coefficient of Aggregate Demand Elasticity is constructed on the polygonal line in ${E}^{n}$. The Coefficient is decomposed and its constituents are revealed. In addition, the convex linear combination coefficients are related to the competitors' market shares and their formal presentation is derived.

Sekulovic, S. The Complete or Total Coefficient of Aggregate Demand Elasticity on a Smooth Arc of the Hyper Curve, Year: 1991

Economic Analysis and Worker's Management, 25()2. Editor: Branko Horvat. Indexed in: Journal of Economic Literature. YU ISSN 0351-286 X

In this work, the construction and interpretation of three economic indicators is laid out. First, the Average Chain Index (ACI) is constructed on a smooth arc of the hyper-curve $\Gamma$. Second, index of real income (which incorporates not only the simultaneous price movements of a set of homogeneous and brand name goods, but also of the nominal income from which their demand is financed) is constructed on a smooth arc of hyper-curve ${\Gamma }^{*}$. Finally, based on the previous findings the primary task is realized: the construction and interpretation of the Complete or Total Coefficient of Aggregate Demand Elasticity on a smooth arc of hyper-curve ${\Gamma }^{*}$.

Fatkic H., Sekulovic S. On ergodic transformations on metric spaces, means by Kolmogorov and Nagumo and means by M. Bajraktarevic, Year: 2007

The Second Bosnian-Herzegovinian Mathematical Conference, International University, , Sarajevo, B&H in: Resume of the Bosnian-Herzegovinian Mathematical Conference, Sarajevo J. Math, Vol 3., No. 2 (2007), 277-278.

Notions of generalized diameters and their connections with ergodic transformations are extended from geometric mean to the means satisfying well-known postulates of A. N. Kolmogorov and M. Nagumo from 1930 and some forms of means introduced by M. Bajraktarevic in 1963 by ${M}_{\phi }\left({t}_{1},\dots ,{t}_{n};f;{q}_{1},\dots ,{q}_{n}\right)={\phi }^{-1}\left(\frac{\sum _{i=1}^{n}{q}_{i}f\left({t}_{i}\right)\phi \left({t}_{i}\right)}{\sum _{i=1}^{n}{q}_{i}f\left({t}_{i}\right)}\right)$ where ${t}_{1},\dots ,{t}_{n}\in \left[\alpha ,\beta \right]\left(\subset ℝ\right)$; ${q}_{1},\dots ,{q}_{n}\in \left(0,\infty \right)$; $\phi \in \Phi ,f\in F$ (wherein $\phi$ respectively $F$ is the set of all continuous strictly monotonic function respectively of all non-negative functions that are different from zero at points $\alpha$ and $\beta$, defined on the segment $\left[\alpha ,\beta \right]$) $\sum _{i=1}^{n}f\left({t}_{i}\right)>0$

The results presented here extend and/or complement the previous results of T. Erber, B. Schweizer and A. Sklar, 1973, R. E. Rice, 1978, C. Sempi, 1985, H. Fatkic, 1987, 1992, 2005, 2006 and also E. Hille, 1965.

• Billingsley, P., Ergodic Theory and Information, John Wiley & Sons, Inc., New York - London - Sydney, 1965.
• Brown, J. R., Ergodic theory and topological dynamics, Academics Press, New York, San Francisco - London, 1976.
• Choe, G. H., Computational Ergodic Theory, Springer, Berlin, 2005.
• Cornfeld, I. P., Fomin, S. V., Sinai, Ya. G., Ergodic Theory, Springer Verlag, New York - Heidelberg - Berlin, 1982.
• Erber, T., Schweizer, B., Sklar, A., Mixing transformations on metric spaces, Comm. Math. Phys., 29(1973), 311-317.
• Erber, T., Sklar, A., Macroscope irreversibility as a manifestation of micro-instabilities. In: Modern Developments in Thermodynamics (B. Gal - Or. e.) pp. 281 - 301. Israel Universities Press and J. Wiley and Sons, Jerusalem - New York, 1974.
• Fatkic, H., On mean values and mixing transformations, in: Proc. Twenty-fourth Internat. Symposium on Functional Equations, Aequationes Math. 32(1987), 104 - 105.
• Fatkic, H., Note on weakly mixing transformations, Aequationes Math. 42(1992), 38 - 44.
• Fatkic, H., On probabilistic metric spaces and ergodic transformations, Ph.D. dissertation, Univ. Sarajevo, 2000, 170 pp; Rad. Mat. 10 (2001)2, 261-263.
• Fatkic, H., Characterizations of measurability-preserving ergodic transformations, Sarajevo J. Math. 1(13)(2005), 49 - 58.
• Fatkic, H., Measurability-preserving weakly mixing transformations, Sarajevo J. Math. Vol. 2, No. 2(2006), 159 - 172.
• Hille, E., Topics in classical analysis, in: Lecture on Modern Mathematics (T. L. Saaty, ed.) Vol 3., Wiley, New York, 1965, pp. 1 - 57.
• Landkof, N. S., Foundations of modern potential theory. Translated from the Russian by A. P. Doohovskoy. Die Grundlehren der mathematischen Wissenschaften, Band 180. Springer - Verlag, New York - Heidelberg, 1972.
• Lesigne, E., Rittaud, B., de la Rue, T., Weak disjointness of measure-preserving dynamical systems, Ergodic Theory Dyn. Syst., 23(4)(2003), 1173 - 1198.
• Martin, N., F., G., On ergodic properties of restriction of inner functions, Ergodic Theory Dyn. Syst., 9(1)(1989), 137 - 151.
• Martin, N., F., G., Conformal isomorphism of inner functions, Ergodic Theory Dyn. Syst., 17(3)(1997), 663 - 666.
• Rice, R., E., On mixing transformations, Aequations Math. 17(1978), 104 - 108.
• Schweizer, B., Sklar, A., Probabilistic metric spaces, Elsevier North - Holand, New York, 1983.
• Sempi, C., On weakly mixing transformations on metric spaces, Rad. Mat. 1(1985), 3 - 7.
• Walters, P., An Introduction to Ergodic Theory, (GTM, Vol. 79), Springer - Verlag, New York - Heidelberg - Berlin, 1982.
Fatkic, H., Sekulovic, S., Fatkic, Hana. Further result on the ergodic transformations that are both strongly mixing and measurability preserving, Year: 2011

The sixth Bosnian-Herzegovinian Mathematical Conference, International University of Sarajevo, , Sarajevo, B&H in: Resume of the Bosnian-Herzegovinian Mathematical Conference, Sarajevo J. Math, Vol 7, No. 2 (2011), 310-311.

In the broadest sense ergodic theory is the study of the qualitative properties of actions of groups on spaces (e.g., measure spaces, or topological spaces, or smooth manifolds). In this work we shall study actions of the group $ℤ$ of integers on a measure space $S$, i.e., we study a transformation $\phi :S\to S$ and its iterates ${\phi }_{n},n\in ℤ$. It is customary in ergodic theory to assume that the underlying space is either a finite or $\sigma$ - finite measure space. We shall assume that the measure is finite. It is commonly further assumed that the measure space is separable. However, we shall not make this assumption, principally because it would rule out some of our principal structure theorems.

Suppose $\left(S,A,\mu \right)$ is a finite measure space. A transformation $\phi :S\to S$ is called:

1. measurable ($\mu$-measurable) if, for any $A$ in $\mathbf{A}$, the inverse image ${\phi }^{-1}$ is in $\mathbf{A}$;
2. measure-preserving if $\phi$ is measurable and $\mu \left({\phi }^{-1}\left(A\right)\right)=\mu \left(A\right)$ for any $A$ in $\mathbf{A}$;
3. ergodic if the only members $A$ of $\mathbf{A}$ with ${\phi }^{-1}\left(A\right)=A$ satisfy $\mu \left(A\right)=0$ or $\mu \left(S\setminus A\right)=0$;
4. (strong-) mixing (with respect to $\mu$) if $\phi$ is $\mu$-measurable and $lim n → ∞ μ ( φ -n ( A ) ∩ B ) = μ ( A ) μ ( B ) μ ( S )$ for any two $\mu$-measurable subsets $A,B$ of $S$. We say that the transformation $\phi :S\to S$ is measurability - preserving (preserves $\mu$-measurability) if, for any $A$ in $\mathbf{A}$, the image $\phi \left(A\right)$ is in $\mathbf{A}$.

Relations between ergodic transformations and Chebyshev functions (as generalizations of Chebyshev polynomials) are investigated. In doing so, notion of $\mathbf{M}$-radius of Chebyshev order $k$ and $\mathbf{M}$-constant of Chebyshev (where $\mathbf{M}≔\left({M}_{n}\right)$ is the power mean) introduced by E. Hille in 1961 (and improved in 1965) are used to prove that even for these quantities the corresponding analogs for ergodic transformations that are both strongly mixing and measurability preserving, proved for diameters in (T. Erber, B. Schweizer and A. Sklar, 1973, R. E. Rice, 1978 and, for geometric diameters, in H. Fatkic; 1987, 2000), hold.

• Billingsley, P., Ergodic Theory and Information, John Wiley & Sons, Inc., New York - London - Sydney, 1965.
• Brown, J. R., Ergodic theory and topological dynamics, Academics Press, New York, San Francisco - London, 1976.
• Choe, G. H., Computational Ergodic Theory, Springer, Berlin, 2005.
• Cornfeld, I. P., Fomin, S. V., Sinai, Ya. G., Ergodic Theory, Springer Verlag, New York - Heidelberg - Berlin, 1982.
• Erber, T., Schweizer, B., Sklar, A., Mixing transformations on metric spaces, Comm. Math. Phys., 29(1973), 311-317.
• Fatkic, H., On mean values and mixing transformations, in: Proc. Twenty-fourth Internat. Symposium on Functional Equations, Aequationes Math. 32(1987), 104 - 105.
• Fatkic, H., Some results on measure-preserving transformations with weak mixing property, Proc. Internat. Conf. on Functional Equations and Inequalities, Koninki, Poland (1991.), Rocznik Naukowo-Dydaktyczny WSP w Krakowie 135, Prace Matematyczne XVII(1992), 9-10.
• Fatkic, H., Note on weakly mixing transformations, Aequationes Math. 42(1992), 38 - 44.
• Fatkic, H., On probabilistic metric spaces and ergodic transformations, Ph.D. dissertation, Univ. Sarajevo, 2000, 170 pp; Rad. Mat. 10 (2001)2, 261-263.
• Fatkic, H., Characterizations of measurability-preserving ergodic transformations, Sarajevo J. Math. 1(13)(2005), 49 - 58.
• Fatkic, H., Measurability-preserving weakly mixing transformations, Sarajevo J. Math. Vol. 2, No. 2(2006), 159 - 172.
• Hewit, E., Stromberg, K., Real and Abstract Analysis, Springer - Verlag, New York - Berlin - Heidelberg - London - Paris - Tokyo - Hong Kong - Barcelona, 1965.
• Hille, E., Topics in classical analysis, in: Lecture on Modern Mathematics (T. L. Saaty, ed.) Vol 3., Wiley, New York, 1965, pp. 1 - 57.
• Landkof, N. S., Foundations of modern potential theory. Translated from the Russian by A. P. Doohovskoy. Die Grundlehren der mathematischen Wissenschaften, Band 180. Springer - Verlag, New York - Heidelberg, 1972.
• Iams, S., Katz, B., Silva, C. E., Street, B., Wickelgren, K., On weakly mixing and double ergodic nonsingular action, Colloq. Math., 103(2)(2005), 247-264.
• James, J., Koberda, T., Lindsey, K., Silva, C. E. Speh, P., On ergodic transformations that are both weakly mixing and uniformly rigid, New York J. Math. 15(2009), 393-403.
• Lesigne, E., Rittaud, B., de la Rue, T., Weak disjointness of measure-preserving dynamical systems, Ergodic Theory Dyn. Syst., 23(4)(2003), 1173 - 1198.
• Rice, R., E., On mixing transformations, Aequations Math. 17(1978), 104 - 108.
• Schweizer, B., Sklar, A., Probabilistic metric spaces, Elsevier North - Holand, New York, 1983.
• Sekulovic, S., Fatkic, H., Mastilovic, A., Structural Identity Formulas and Series with Application to Elasticity with the Statistical Index, in: Zbornik radova Naučnog skupa - Prva matematička konferencija Republike Srpske (s međunarodnim učešćem), 21. i 22. maj 2011., Pale, B&H.; Naučni skupovi, Vol. 6/3 (2012), pp. 227-242.
• Sempi, C., On weakly mixing transformations on metric spaces, Rad. Mat. 1(1985), 3 - 7.
• Walters, P., An Introduction to Ergodic Theory, (GTM, Vol. 79), Springer - Verlag, New York - Heidelberg - Berlin, 1982.
Sekulovic, S., Fatkic, H., Mastilovic, A., Structural Identity Formulas and Series with Application to Elasticity with the Statistical Index, Year: 2011

in: Proceedings of the 1st Mathematical Conference of Republic of Srpska - Section of Applied Mathematics, Pale, B&H, pp. 226-242,

Excerpt from the review: The work is very interesting, mathematically correct, large enough, very applicable and therefore it is strongly recommended for publishing. The authors first define formulas that are called the Structural Identity Formulas (SIF), and then have proved SIF Theorem: $\left(\forall m\in ℕ\setminus \left\{1\right\}\right)$ the sum of all SIF is equal to one. Four interpretations of the SIF are elaborated and they include: (i) the SIF and the Figurate numbers, (ii) the geometrical interpretation, (iii) a technical interpretation, and (iv) the statistical interpretation ... There is a considerable evidence to support a conjecture that the result obtained in this work (tightly related to the concept of the Complete or Total Coefficient of Aggregate Demand Elasticity, initially developed in ${ℝ}^{n}$ with the usual or standard metric/norm) can be applied and extended to more generalized situation - to probabilistic normed (PN) spaces in the sense of C. Alsina, B Schweizer and A. Sklar. PN spaces are real linear spaces in which the norm of each vector is an appropriate probability distribution function rather than a number. Such spaces were first introduced by A. N. Serstnev Dokl. Akad. Nauk SSSR 149 (1963), 280-283, ...

Available at: Research Gate

Fatkic, H., Sekulovic, S., Fatkic, Hana, Probabilistic Metric Spaces Determined by Weakly Mixing Transformations, Year: 2012

The Second Mathematical Conference of Republic of Srpska, Trebinje,

In this paper we investigate the probabilistic metric spaces determined by the weakly mixing (WM) transformations (a probabilistic metric space is a generalization of metric space (briefly a PM space), in which the "distance" between any two points is a probability distribution function rather than the number). Continuing the work begun by B. Schweizer and N. Sklar (Probabilistic metric spaces determined by measure-preserving transformations, Z. Wahrsch. Verw. Geb. 26(1973), 235-239), we construct a new class of PM spaces. Specifically, we prove that if $\left(S,d\right)$ is a separable metric space endowed with probability measure $P$ and if $T$ is a transformation on $S$, that is weakly mixing with respect to $P$, than for any $x>0$ and almost all pairs of points $\left(p,q\right)$ in ${S}^{2}$ there is a distribution function $F$ such that the average number of times in the first $\left(n-1\right)$ iterations of $T$ that the distance between the points ${T}^{n}\left(p\right)$ and ${T}^{n}\left(q\right)$ is less than $x$ converges to $F\left(x\right)$ as $n$ goes to infinite. The collection of these distribution functions is almost an equilateral probabilistic pseudometric space and the transformation $T$ is (probabilistic) distance-preserving on this space.

The above ideas play important role in the distributional chaos theory. The results presented here also extend and/or complement the previous results of T. Erber, B. Schweizer and A. Sklar (Mixing transformations on metric spaces, Comm. Math. Phys., 29(1973), 311-317), R. E. Rice (On mixing transformations, Aequations Math. 17(1978), 104-108), H. Fatkic (Note on weakly mixing transformations, Aequations Math. 42(1998)38-44; Characterization of measurability-preserving ergodic transformations, Sarajevo, J. Math. 1(13)(2005), 49-58; Measurability-preserving weakly mixing transformations, Sarajevo J. Math., Vol. 2, No. 2 (2006), 159-172), H. Fatkic and S. Sekulovic (On ergodic transformations on metric spaces, means by Kolmogorov and Nagumo and means by M. Bajraktarevic), and R. Pikula (On some notions of chaos in dimension zero, Colloq. Math. 107(2007), 167-177).

Huse Fatkic, Slobodan Sekulovic, Hana Fatkic On harmonic Mean Values and Weakly Mixing Transformations, Year: 2014

Huse Fatkic, Department of Mathematics, Faculty of Electrical Engineering, University of Sarajevo, B&H; Slobodan Sekulovic, Hot Springs National Park, Arkansas, USA; Hana Fatkic, Department of Computer Science and Informatics, Faculty of Electrical Engineering, University of Sarajevo, B&H; hfatkic@etf.unsa.ba, slobodan.sekulovic@gmail.com, fatkic.hanna@gmail.com

Let $\left(S,d\right)$ be an extended metric space, and let $A$ be a subset of $S$. For any positive integer $k\left(k\ge 2\right)$, we define the harmonic diameter of order $k$ of $A$, denoted by ${D}_{k}\left(A\right)$, by Note that ${D}_{2}\left(A\right)$ is the ordinary diameter of the set $A$. The main result of this work is the following theorem: For the above situation if $\left(S,A,P\right)$ is a probability space with the property that every open ball in $\left(S,d\right)$ is $P$-measurable and has positive measure, and if $\phi$ is transformation on $S$, that is weakly mixing with respect to $P$, and $A$ is $P$-measurable with $P\left(A\right)>0$, than $\underset{x\to \infty }{\mathrm{lim}}\mathrm{sup}{D}_{k}\left({\phi }^{n}\left(A\right)\right)={D}_{k}\left(S\right)$.

The above theorem shows that, under iteration, all weakly mixing transformations tend to spread the sets out, not only in terms of the ordinary diameter, but also in terms of the harmonic diameter of any finite order. Thus, even though some set A may not spread out in "volume" (measure), there is a very definite sense that $A$ does not remain small. This mixing character of the weakly mixing transformations (e. g., of the polynomials ${C}_{n}\phantom{\rule{0.2em}{0ex}}\left(n=0,1,2,\dots \right)$, defined on the interval $\left[2,2\right]$ by ${C}_{n}\left(x\right)=2\mathrm{cos}\left(n\mathrm{arccos}\left(x/2\right)\right)$, which are related to the standard Chebyshev polynomials), inter alia, can be used for developing an efficient method for generating sequences of pseudo-random numbers (computer runs on selected pairs of points; the results obtained with ${C}_{10}$ as transformation $\phi$ indicate that the convergence of the corresponding sequences of the second moments about the mean (variances) to the second moment of corresponding distribution function is fairly rapid).

The obtained results extend and/or complement the previous results due to:

• Rice, Roy E., On mixing transformations, Aequationes Math. 17 (1978), 104-108.
• Erber, Thomas; Schweizer, Berthold; Sklar, Abe, Mixing transformations on metric spaces, Comm. Math. Phys. 29 (1973) 311-317. Grigor'evich.
• Fatkic, Huse; Brkic, Mehmed, Strongly mixing transformations and geometric diameters, Sarajevo J. Math 8 (21) (2012), no. 2, 245-257.
• Landkof, Neum S. (Samoilovich), Foundations of modern potential theory. Translated from Russian by A. P. Doohovskoy. Die Grundlehren der Wissenschaften, Band 180. Springer-Verlag, New York - Heidelbrg, 1972.
• Saff, Edward B., Logarithmic potential theory with applications to approximation theory, Surv. Approx. Theory 5 (2010), 165-200.
• Sempi, Carlo, On weakly mixing transformations on metric spaces, Rad.Mat. 1 (1985), 3-7.

There is considerable evidence to support a conjecture that our result (for weakly mixing transformations/weakly mixing dynamical systems with discrete time) can be extended to weakly mixing dynamical systems with continuous time.

Sekulovic S., Fatkic Hana, On Some Elements of the Theory of Composite Index Numbers, Year: 2015

The fifth mathematical conference of the Republic of Srpska, Trebinje, Bosnia and Herzegovina, Slobodan Sekulovic, Hot Springs National Park, Arkansas, USA Hana Fatkic, Department of Computer Science and Informatics, Faculty of Electrical Engineering University of Sarajevo, B&H

In this paper we investigate the notions and the properties of three Composite index numbers (Composite indices are unweighted price indices (UPI) designed for monitoring the general price-level movements of an industry, or a part of it: (i) Average Base Index (ABI), (ii) Average Chain Index (ACI), and (iii) Average of Relative-Variation Price Relatives (ARVPR)). The exposition goes to the extent from which further evolution of the said indices becomes interwoven with the evolution of the concept name The Complete or Total Coefficient of Aggregate Demand Elasticity (see [5] - [7]). In the that respect, we define said indices on the set of real numbers, and in normed vector space, we analyze their complex structure which springs from the relative - variation price relatives, and establish their dependability (j) from the perspective of their "end-use domain", and (jj) in terms of meeting the mathematical tests: the time-reversal test (ABI & ACI are reversible) and cyclical or circular test.

The results presented in this paper extend and/or complement the results presented by Blazic (see Milos R. Blazic, Opšta Statistika, Osnovi i Analiza, Savremena Administracija, Beograd, 1977, pp 187-192).

References:

• Blazic, M., Opšta Statistika - Osnovi i Analiza, Savremena Administracija, Beograd, 1977.
• Fatkic, H., Fatkic, B., Karahodzic, V., On generalized harmonic diameters and some classes of measure-preserving transformations The Fifth Mathematical Conference of Republic of Srpska - Section for Analysis and Probability & Statistics, Trebinje, Bosnia and Herzegovina, June 5&6, 2015.
• Fatkic, H., Fatkic, J., Brkic, M., On the various notions of recurrence for some classes of nonsingular transformations, The Fifth Mathematical Conference of Republic of Srpska - Section for Analysis and Probability & Statistics, Trebinje, Bosnia and Herzegovina, June 5&6, 2015.
• Fatkic, Hana, Sklar, A., Fatkic, H., Dispersion Under Iteration of Strongly Mixing Transformations on Metric Spaces, International Journal of Applied Mathematics, Electronics and Computers (IJAMEC), 3(3)(2015), 150-154.
• Sekulovic, S., The Complete or Total Coefficient of Aggregate Demand Elasticity, Economic Analysis and Workers' Management 23(1989)2. (Editor: Branko Horvat)
• Sekulovic, S., The Generalization of the Complete or Total Coefficient of Aggregate Demand Elasticity, Economic Analysis and Workers' Management, 25(1991)3. (Editor: Branko Horvat)
• Sekulovic, S., The Complete or Total Coefficient of Aggregate Demand Elasticity on a Smooth Arc of the Hyper Curve, Economic Analysis and Workers' Management 25(1991)3 (Editor: Branko Horvat)
• Sekulovic, S., Fatkic, H., Mastilovic, A., Structural Identity Formulas and Series With Application to Elasticity With the Statistical Index, In: Proceedings of the 1st Mathematical Conference of Republic of Srpska - Section of Applied Mathematics, Pale, B&H, pp. 226-242, 2011.
Pending: Sekulovic, S. General Theory of Complete or Total Coefficient of Aggregate Demand Elasticity and Some Composite Indices

The book contains three chapters, named after three (earlier published) follow-up papers (Sekulovic, 1989, 1990, 1991) and two appendices. Its core remains faithful to the idea conceived and laid out in those papers; The Complete or Total Coefficient of Aggregate Demand Elasticity incorporates (as opposed to the partial elasticity coefficients) simultaneous variation of all independent variables (prices), in order to reflect the relative variation in aggregate demand. However, the chapters are modestly rearranged, definitions and theorems are improved, and the concept is broadened so as to bring us close to the point when generating the analytical formulas of the demand functions for the competitive and brand name products becomes conditioned by a new concept called the Fractional Market Shares. The first appendix provides an introductory exposition of the theory of three Composite indices, to the extent from which their further evolution becomes interwoven with the evolution of the concept of Complete or Total Coefficient of Aggregate Demand Elasticity.

Pending: Sekulovic, S. New Methods of Measurement and Positioning Against the Competitors

This comprehensive theoretical research will offer new methods (tools) of measurement and positioning against the competitors. Emphasis will be on the applications of these methods in aviation industry.

Sekulovic, S., Fatkic, H., Elements of the Theory of Fractional Market Shares - Expressing Market Shares of the Competitors Through the Convex Linear Combination Coefficients

The Sixth Mathematical Conference of Republic of Srpska - Section for Applied Mathematics, Pale, Bosnia and Herzegovina,

This paper constitutes our attempt to cast an unconventional viewpoint upon the firm's market share. More concretely put, the competitors' market share constitute the "Complete or Total Coefficient of Aggregate Demand Elasticity" (Sekulovic, [3] and [4]), and except for simple analogy with convex linear combination coefficients (e.g., each one is larger than zero and their sum is equal to one) no deeper bridge-building effort between these two notions has been made. Therefore, we pursue this investigation by introducing the Fractional Market Shares (FMS) concept first, and then proceed to elaboration of the analytical formulas through which the convex linear combination coefficients can be expressed. The revealed properties demonstrate how seemingly unrelated and distant notions such as the firms' market shares and the convex linear combination coefficients can be linked.

The paper represents a segment of the research in progress by the name: The Theory of Fractional Market Shares.

• Baumol, William J., Panzar, John, C., and Willig, Robert, D. (1982), Contestable Market and the Theory of Industry Structure (San Diego: Harcourt Brace Jovanovich, Inc.).
• Baumol, William J., Panzar, John, C., and Willig, Robert, D. (1986), On the Theory of Perfectly Contestable Markets, in: J. Stiglitz and F. Mathewson, eds., New developments in the analysis of market structure, Cambridge: MIT Press.
• Sekulovic, S. (1989), The Complete or Total Coefficient of Aggregate Demand Elasticity, Economic Analysis and Workers' Management 23(1989)2.
• Sekulovic, S. (1990), The Generalization of the Complete or Total Coefficient of Aggregate Demand Elasticity, Economic Analysis and Workers' Management 24(1990)4.
• Sekulovic, S., Fatkic, H., Mastilovic, A. (2011), Structural Identity Formulas and Series with Application to Elasticity with the Statistical Index, in: Proceedings of the 1st Mathematical Conference of Republic of Srpska - Section of Applied Mathematics, Pale, B&H, pp. 226-242.