Characterizations of Higher Order Strongly Generalized Convex Functions

Muhammad Aslam Noor (), Khalida Inayat Noor () and Michael Th. Rassias ()
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Muhammad Aslam Noor: COMSATS University Islamabad
Khalida Inayat Noor: COMSATS University Islamabad
Michael Th. Rassias: University of Zurich

A chapter in Nonlinear Analysis, Differential Equations, and Applications, 2021, pp 341-364 from Springer

Abstract: Abstract In this paper, we define and consider some new concepts of the higher order strongly generalized convex functions with respect to two arbitrary functions. Some properties of the higher order strongly generalized convex functions are investigated under suitable conditions. It is shown that the operator parallelogram laws for the characterization of uniformly Banach spaces can be obtained as a novel applications of higher order strongly affine functions. It is shown that the optimality conditions of the higher order strongly generalized convex functions are characterized by a new class of variational inequalities. Some special cases also discussed. Results obtained in this paper can be viewed as significant refinement and improvement of previously known results.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-72563-1_15

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DOI: 10.1007/978-3-030-72563-1_15

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