Characterizations of higher order strongly generalized convex functions
type: Item
instance of: scholarly article
title: Characterizations of higher order strongly generalized convex functions
zbMATH Open document ID: 1483.46075
DOI: 10.1007/978-3-030-72563-1_15
author: Khalida Inayat Noor
author: Muhammad Aslam Noor
author: Michael Th. Rassias
publication date: 2021-09-07T00:00:00Z
review text: Consider a Hilbert space \(H\) and two transformations of the space, \(g,h:H\rightarrow H\). The authors extend the concepts of convex set and convex function by considering the behaviour of the function in the presence of the two transformations \(g\) and \(h\) of its domain. They obtain the concept of \((g,h)\)-convex subset of \(K\subseteq H\) as a set containing the point \({(1-t)h(x)}+tg(y)\), whenever \(x,y\in K\) and \(t\in [0,1]\). The properties of convexity, strong convexity, quasi-convexity, log-convexity of functions are extended in this framework of \((g,h)\)-convexity. Characterizations of each type of generalized convex functions are given. It is shown that the optimality conditions are characterized by a new class of variational inequalities in the class of generalized strongly convex functions. The operator parallelogram laws for the characterization of uniform Banach spaces are obtained as an applications of the generalized affine functions in the framework provided by the double transformation of the space using the pair \((g,h)\). For the entire collection see [Zbl 1471.34005].
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 46N10
Mathematics Subject Classification ID: 52A30
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 7392150
zbMATH Keywords: strong \((h,g)\)-convex function
zbMATH Keywords: strong \((h,g)\)-convex set
zbMATH Keywords: parallelogram law
zbMATH Keywords: variational inequality
MaRDI profile type: Publication
full work available at URL: 978-3-030-72563-1 15
OpenAlex ID: W3193936248
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description: scientific article; zbMATH DE number 7392150