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.
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.
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.
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.
Based on the strong stationary condition, we formulate second-order and higher order duals for a mathematical program with complementary constraints (MPCC). Under suitable generalizedconvexity assumptions, we then pr...
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Based on the strong stationary condition, we formulate second-order and higher order duals for a mathematical program with complementary constraints (MPCC). Under suitable generalizedconvexity assumptions, we then propose several duality theorems for second and higher order duality in MPCC problems, including the weak duality, strong duality, converse duality, and strict converse duality theorems. Moreover, we present examples to illustrate these results, where one of them reveals that a lower bound provided by our proposed second-order duality is tighter than the one given by the first-order duality.
Some properties of sigma-convexfunctions are studied. Then some relations between the notions of sigma-subdifferentials and sigma-convexfunctions are established. Also, we present some results regarding the sum form...
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Some properties of sigma-convexfunctions are studied. Then some relations between the notions of sigma-subdifferentials and sigma-convexfunctions are established. Also, we present some results regarding the sum formula for the sigma-subdifferential. Moreover, we obtain some particular relationships between the sigma-subdifferential and the (sigma, y)-conjugate. Finally, by imposing some assumptions on f and sigma, the maximal 2 sigma-monotonicity of sigma-subdifferential is studied. Indeed, the maximality of the usual Fenchel subdifferentials of lower semicontinuous convexfunctions follows from our result.
The notion of s-monotone polarity for s-subdifferential is introduced and studied. Also, the concept of Frechet s-subdifferential is introduced and then some results regarding this concept are obtained. In addition, s...
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The notion of s-monotone polarity for s-subdifferential is introduced and studied. Also, the concept of Frechet s-subdifferential is introduced and then some results regarding this concept are obtained. In addition, some particular relationships between the s-subdifferential and Frechet s-subdifferential are presented.
We introduce and study the notion of e-subdifferential for an e-convex function in locally convex spaces. Some relationships between the e-subdifferential and the Clarke-Rockafellar subdifferential are established. Be...
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We introduce and study the notion of e-subdifferential for an e-convex function in locally convex spaces. Some relationships between the e-subdifferential and the Clarke-Rockafellar subdifferential are established. Besides, the e-convexfunctions are characterized. Moreover, some results regarding the locally Lipschitz properties of e-convexfunctions are obtained.
In this paper we deal with functions related to generalizedconvexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convexfunctions, stro...
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In this paper we deal with functions related to generalizedconvexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convexfunctions, strongly convexfunctions as well as superquadratic functions.
In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Hol...
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In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Holder's and Power-mean integral inequalities, we develop some new fractal-fractional Simpson's type inequalities. Furthermore, we use modified Yang Holder's and Power-mean inequality to create new fractal estimates. We also give comparison analysis of bounds and show how the modified form of Yang Holder's and Power-mean integral inequalities can result in improved lower upper bounds. We also provide concrete examples to examine the validity of obtain results numerically and also justify them by 2D and 3D graphical analysis. As implementations, we operate our findings to get new applications in form of..-type special means, moment of random variables and wave equations.
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