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.
The notion of strongly n-convexfunctions with modulus c > 0 is introduced and investigated. Relationships between such functions and n-convexfunctions in the sense of Popoviciu as well as generalizedconvex funct...
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The notion of strongly n-convexfunctions with modulus c > 0 is introduced and investigated. Relationships between such functions and n-convexfunctions in the sense of Popoviciu as well as generalized convex functions in the sense of Beckenbach are given. Characterizations by derivatives are presented. Some results on strongly Jensen n-convexfunctions are also given. (C) 2010 Elsevier Ltd. All rights reserved.
Some properties of strongly convexfunctions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers-Ulam stability result for strongly convexfunctions ...
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Some properties of strongly convexfunctions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers-Ulam stability result for strongly convexfunctions are given. An integral Jensen-type inequality and a Hermite-Hadamard-type inequality for strongly convexfunctions are obtained. Finally, a relationship between strong convexity and generalizedconvexity in the sense of Beckenbach is shown.
A new class of generalized convex functions, called the functions with pseucloconvex sublevel sets, is defined. They include quasiconvex ones. A complete characterization of these functions is derived. Further, it is ...
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A new class of generalized convex functions, called the functions with pseucloconvex sublevel sets, is defined. They include quasiconvex ones. A complete characterization of these functions is derived. Further, it is shown that a continuous function admits pseudoconvex sublevel sets if and only if it is quasiconvex. Optimality conditions for a minimum of the nonsmooth nonlinear programming problem with inequality, equality and a set constraints are obtained in terms of the lower Hadamard directional derivative. In particular sufficient conditions for a strict global minimum are given where the functions have pseudoconvex sublevel sets. (c) 2008 Elsevier Inc. All rights reserved.
We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]...
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We introduce two pairs of nondifferentiable multiobjective second order symmetric dual problems with cone constraints over arbitrary closed convex cones, which is different from the one proposed by Mishra and Lai [12]. Under suitable second order pseudo-invexity assumptions we establish weak, strong and converse duality theorems as well as self-duality relations. Our symmetric duality results include an extension of the symmetric duality results for the first order case obtained by Kim and Kim [7] to the second order case. Several known results are abtained as special cases.
We introduce a pair of multiobjective generalized second order symmetric dual programs where the objective function contains a support function. Weak, strong and converse duality theorems for these second order proble...
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We introduce a pair of multiobjective generalized second order symmetric dual programs where the objective function contains a support function. Weak, strong and converse duality theorems for these second order problems are established under suitable generalized second order convexity assumptions. Also, we give some special cases of our second order symmetric duality results.
In this paper, we are concerned with a nondifferentiable minimax fractional problem with inequality constraints. We introduce a new class of generalizedconvex function, that is, nonsmooth generalized (F, rho, theta)-...
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In this paper, we are concerned with a nondifferentiable minimax fractional problem with inequality constraints. We introduce a new class of generalizedconvex function, that is, nonsmooth generalized (F, rho, theta)-d-univex function. In the framework of the new concept, we derive Kuhn-Tucker type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different types of dual problems. (c) 2006 Elsevier Inc. All rights reserved.
A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,the...
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A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,theta,rho,d)-convex class about the Clarke's generalized gradient. Under the above generalizedconvexity assumption, necessary and sufficient conditions for optimality are given. Finally, a dual problem corresponding to (MFP) is formulated, appropriate dual theorems are proved.
A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,the...
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A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,theta,rho,d)-convex class about the Clarke's generalized gradient. Under the above generalizedconvexity assumption, necessary and sufficient conditions for optimality are given. Finally, a dual problem corresponding to (MFP) is formulated, appropriate dual theorems are proved.
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