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Author Country (or Countries)

Pakistan.

Abstract

In this paper, we define and introduce some new concepts of the higher order strongly-generalized convex functions involving an arbitrary function. Some properties of the higher order strongly-generalized convex functions are investigated under suitable conditions. We have proved that the optimality conditions of higher order strongly generalized can be characterized by a class of variational inequalities, which is called higher-order strongly variational inequality. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher-order strongly-generalized affine convex functions. Results obtained in this paper can be viewed as refinement and improvement of previously-known results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140117

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