Generalized Preinvex Functions and Their Applications

Kılıçman, Adem; Saleh, Wedad

doi:10.3390/sym10100493

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…Later, the same authors [18] obtained necessary optimality conditions for an optimization problem on complete Riemannian manifolds, but they did not obtain characterizations. Kiliçman and Saleh [19] presented a Karush-Kuhn-Tucker sufficient optimality condition as well as a new Hermite-Hadamard-type integral inequality using differentiable sub-b-s-preinvex functions.…”

Section: Introductionmentioning

confidence: 99%

Solutions of Optimization Problems on Hadamard Manifolds with Lipschitz Functions

2020

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The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush–Kuhn–Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash’s critical and equilibrium points coincide in the case of invex payoff functions. This is done on Hadamard manifolds, a particular case of noncompact Riemannian symmetric spaces.

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Section: Introductionmentioning

confidence: 99%

Solutions of Optimization Problems on Hadamard Manifolds with Lipschitz Functions

2020

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“…One example of these is how the convexity was applied to estimate errors when using a trapezoidal formula for numerical integration [6,7]. Others include studying problems in nonlinear programming and applying them to special means [8]. Among them, an interesting inequality for convex function is of Hermite-Hadamard type, which can be stated as follows:…”

Section: Introductionmentioning

confidence: 99%

Some Integral Inequalities for h-Godunova-Levin Preinvexity

Almutairi

Kılıçman

2019

Symmetry

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In this study, we define new classes of convexity called h-Godunova-Levin and h-Godunova-Levin preinvexity, through which some new inequalities of Hermite-Hadamard type are established. These new classes are the generalization of several known convexities including the s-convex, P-function, and Godunova-Levin. Further, the properties of the h-Godunova-Levin function are also discussed. Meanwhile, the applications of h-Godunova-Levin Preinvex function are given.

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“…Hermite-Hadamard inequality based on log-preinvex function was presented by Noor [7,8]. Many papers have appeared in the literature under the concept of preinvexity (see, [9][10][11][12][13][14][15]).…”

Section: Introductionmentioning

confidence: 99%