Generalized Jensen-Mercer inequality for functions with nondecreasing increments
type: Item
instance of: scholarly article
title: Generalized Jensen-Mercer inequality for functions with nondecreasing increments
zbMATH Open document ID: 1471.26009
DOI: 10.1155/2016/5231476
author: Asif R. Khan
author: S. Saadi
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: In [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 4, Paper No. 73, 2 p. (2003; Zbl 1048.26016)], \textit{A. McD. Mercer} established an interesting variation of Jensen's inequality and later in 2009 Mercer's result was generalized to higher dimensions by \textit{M. Niezgoda} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 2771--2779 (2009; Zbl 1177.26016)]. Recently, Asif et al. has stated an integral version of Niezgoda's result for convex functions. We further generalize Niezgoda's integral result for functions with nondecreasing increments and give some refinements with applications. In the way, we generalize an important result, Jensen-Boas inequality, using functions with nondecreasing increments. These results would constitute a valuable addition to Jensen-type inequalities in the literature.
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 6929370
Wikidata QID: Q59121535
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/5231476
OpenAlex ID: W2520627638
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description: scientific article; zbMATH DE number 6929370