In this paper, (alpha, phi, Q)-invexity is introduced, where alpha: X x X --> int R+m, phi: X x X --> X, X is a Banach space, Q is a convex cone of R(m). This unifies the properties of many classes of functions,...
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In this paper, (alpha, phi, Q)-invexity is introduced, where alpha: X x X --> int R+m, phi: X x X --> X, X is a Banach space, Q is a convex cone of R(m). This unifies the properties of many classes of functions, such as Q-convexity, pseudo-linearity, representation condition, null space condition, and V-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (alpha, phi, Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (alpha, phi, Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.
We introduce and study the notion of the (sigma, y)-conjugate of a proper sigma-convex function. Some relations between the sigma-subdifferentials and the Clarke-Rockafellar subdifferential are established. Also, we p...
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We introduce and study the notion of the (sigma, y)-conjugate of a proper sigma-convex function. Some relations between the sigma-subdifferentials and the Clarke-Rockafellar subdifferential are established. Also, we present some results regarding the sigma-monotonicity of the sigma-subdifferential of a function and its sigma-convexity. Moreover, we obtain some particular relationships between the sigma-subdifferential and the (sigma, y)-conjugate.
We introduce and study the notion of sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgree...
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We introduce and study the notion of sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-subdifferential of a proper function f which contains the Clarke-Rockafellar subdifferential of f under some mild assumptions on f and sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We show that some well known properties of the convex function, namely Lipschitz property on the interior of its domain, remain valid for the large class of sigma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}-convexfunctions.
The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363-371] is extended to the two-dimensional case. Using three-param...
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The concept of generalized convex functions introduced by Beckenbach [E.F. Beckenbach, generalized convex functions, Bull. Amer. Math. Soc. 43 (1937) 363-371] is extended to the two-dimensional case. Using three-parameter families, we define generalizedconvex (midconvex, M-convex) functions f : D subset of R-2 -> R and show some continuity properties of them. (c) 2006 Elsevier Inc. All rights reserved.
Properties of generalized convex functions, defined in terms of the generalized means introduced by Hardy, Littlewood, and Polya, are easily obtained by showing that generalized means and generalized convex functions ...
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In this paper, we establish a new local fractional integral identity involving three point by the use of Peano kernel approach. Using this identity we derive some new local fractional integrals inequalities of Maclaur...
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In this paper, we establish a new local fractional integral identity involving three point by the use of Peano kernel approach. Using this identity we derive some new local fractional integrals inequalities of Maclaurin -type for functions whose local fractional derivatives are generalized convex functions. In order to show the effectiveness of the obtained results, we apply them in numerical integration and to special means.
In this paper, we introduce and study a new class of generalizedfunctions, called generalized geometrically convexfunctions. We establish several basic inequalities related to generalized geometrically convex functi...
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In this paper, we introduce and study a new class of generalizedfunctions, called generalized geometrically convexfunctions. We establish several basic inequalities related to generalized geometrically convexfunctions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convexfunctions. Several special cases are discussed, which can be deduced from our main results.
It is proved that for a rationally s-convex function continuity and local s-HOLDER-continuity are equivalent at each interior point of the domain of definition of the function. Furthermore, it is shown that a rational...
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In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a tran...
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In this paper, we study the effects of a linear transformation on the partial order relations that are generated by a closed and convex cone in a finite-dimensional space. Sufficient conditions are provided for a transformation preserving a given order. They are applied to derive the relationship between the efficient set of a set and its image under a linear transformation, to characterize generalizedconvex vector functions by using order-preserving transformations, to establish some calculus rules for the subdifferential of a convex vector function, and develop an optimality condition for a convex vector problem.
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized...
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In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.
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