\(q\)-Hermite-Hadamard inequalities for generalized exponentially \((s,m;\eta)\)-preinvex functions
type: Item
instance of: scholarly article
title: \(q\)-Hermite-Hadamard inequalities for generalized exponentially \((s,m;\eta)\)-preinvex functions
zbMATH Open document ID: 1477.26042
DOI: 10.1155/2021/5577340
author: Yanyan Li
published in: Journal of Mathematics
publication date: 2021-06-28T00:00:00Z
review text: Summary: In this article, we introduce a new extension of classical convexity which is called generalized exponentially \((s,m;\eta)\)-preinvex functions. Also, it is seen that the new definition of generalized exponentially \((s,m;\eta)\)-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new \({}^{m \kappa_2} q\)-integral identity for the twice \({}^{m \kappa_2}q\)-differentiable function. By using this identity, we show essential new results for Hermite-Hadamard-type inequalities for the \({}^{m \kappa_2}q\)-integral by utilizing differentiable exponentially \((s,m;\eta)\)-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7363799
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5577340
OpenAlex ID: W3156250491
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description: scientific article; zbMATH DE number 7363799