In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or...
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In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or in the polar coordinate system in domains on the plane. We establish a connection of such functions with functions that are convex with respect to solutions of second-order linear differential equations, that is, convex with respect to two functions.
In this paper, a general local fractional integral identity on fractal set R-alpha (0 < alpha <= 1) is established. We obtain some general local fractional integral inequalities for twice differentiable generali...
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In this paper, a general local fractional integral identity on fractal set R-alpha (0 < alpha <= 1) is established. We obtain some general local fractional integral inequalities for twice differentiable generalized convex functions. Based on these results, we derive some special inequalities. Some applications to error estimations for numerical integration and to special means are also given.
Employing some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for local (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization pro...
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Employing some advanced tools of variational analysis and generalized differentiation, we establish necessary conditions for local (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with an infinite number of inequality constraints. Sufficient conditions for such solutions to the considered problem are also obtained by means of proposing the use of (strictly) generalized convex functions. In addition, we state a dual problem to the primal one and explore duality relations. (C) 2016 Elsevier B.V. All rights reserved.
This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalizedconvex func...
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This paper aims at studying optimality conditions of robust weak efficient solutions for a nonsmooth uncertain multi-objective fractional programming problem(NUMFP).The concepts of two types of generalized convex function pairs,called type-I functions and pseudo-quasi-type-I functions,are introduced in this paper for(NUMFP).Under the assumption that(NUMFP)satisfies the robust constraint qualification with respect to Clarke subdifferential,necessary optimality conditions of the robust weak efficient solution are *** optimality conditions are obtained under pseudo-quasi-type-I generalizedconvexity ***,we introduce the concept of robust weak saddle points to(NUMFP),and prove two theorems about robust weak saddle *** main results in the present paper are verified by concrete examples.
We introduce and investigate a new generalizedconvexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly...
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We introduce and investigate a new generalizedconvexity notion for functions called prox-convexity. The proximity operator of such a function is single-valued and firmly nonexpansive. We provide examples of (strongly) quasiconvex, weakly convex, and DC (difference of convex) functions that are prox-convex, however none of these classes fully contains the one of prox-convexfunctions or is included into it. We show that the classical proximal point algorithm remains convergent when the convexity of the proper lower semicontinuous function to be minimized is relaxed to prox-convexity.
In this paper we introduce a new monotonicity concept for multivalued operators, respectively, a new convexity concept for real valued functions, which generalize several monotonicity, respectively, convexity notions ...
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In this paper we introduce a new monotonicity concept for multivalued operators, respectively, a new convexity concept for real valued functions, which generalize several monotonicity, respectively, convexity notions already known in literature. We present some fundamental properties of the operators having this monotonicity property. We show that if such a monotonicity property holds locally then the same property holds globally on the whole domain of the operator. We also show that these two new concepts are closely related. As an immediate application we furnish some surjectivity results in finite dimensional spaces.
Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive fiel...
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Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convexfunctions. In this paper, we employ linear fractals R alpha to investigate the (s,m)-convexity and relate them to derive generalized Hermite-Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s,m)-convexfunctions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper.
The present article addresses the concept ofp-convexfunctions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the g...
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The present article addresses the concept ofp-convexfunctions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers arep-convex. The method we present is an alternative in showing the classical variants associated with generalizedp-convexfunctions. Some parts of our results cover the classical convexfunctions and classical harmonically convexfunctions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.
We introduce a family of genuine Bernstein-Durrmeyer type operators preserving the functions 1 and x(j). For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is...
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We introduce a family of genuine Bernstein-Durrmeyer type operators preserving the functions 1 and x(j). For them, we establish Voronovskaja type formulas. The behaviour with respect to generalized convex functions is investigated.
The Hardy-Littlewood-Polya majorization theorem is extended to the framework of some spaces with a curved geometry (such as the global NPC spaces and the Wasserstein spaces). We also discuss the connection between our...
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The Hardy-Littlewood-Polya majorization theorem is extended to the framework of some spaces with a curved geometry (such as the global NPC spaces and the Wasserstein spaces). We also discuss the connection between our concept of majorization and the subject of Schur convexity. Several applications are included. (C) 2013 Elsevier Inc. All rights reserved.
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