Uniform treatment of Jensen's inequality by Montgomery identity
type: Item
instance of: scholarly article
title: Uniform treatment of Jensen's inequality by Montgomery identity
zbMATH Open document ID: 1477.26039
DOI: 10.1155/2021/5564647
author: Tahir Rasheed
author: S. I. Butt
author: Đilda Pečarić
author: Ahmet Ocak Akdemir
author: J. Pečarić
published in: Journal of Mathematics
publication date: 2021-07-07T00:00:00Z
review text: Summary: We generalize Jensen's integral inequality for real Stieltjes measure by using Montgomery identity under the effect of \(\mathfrak{n}\)-convex functions; also, we give different versions of Jensen's discrete inequality along with its converses for real weights. As an application, we give generalized variants of Hermite-Hadamard inequality. Montgomery identity has a great importance as many inequalities can be obtained from Montgomery identity in \(q\)-calculus and fractional integrals. Also, we give applications in information theory for our obtained results, especially for Zipf and Hybrid Zipf-Mandelbrot entropies.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 7369041
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5564647
OpenAlex ID: W3162766251
cites work: Jensen‐Grüss inequality and its applications for the Zipf‐Mandelbrot law
cites work: New refinement of the Jensen inequality associated to certain functions with applications
cites work: A new bound for the Jensen gap pertaining twice differentiable functions with applications
cites work: On generalized Ostrowski-type inequalities for functions whose first derivatives absolute values are convex
cites work: Q4432165
cites work: Q3146344
cites work: Bounds on the deviation of a function from its averages
cites work: Q4933986
cites work: On some inequalities for convex functions of higher order. II
cites work: Q2972729
cites work: Q4905200
cites work: Linear operators inequality for $n$-convex functions at a point
cites work: \((\mathrm{p,q})\)-analysis of Montgomery identity and estimates of \((\mathrm{p,q})\)-bounds with applications
cites work: A descent SQP alternating direction method for minimizing the sum of three convex functions
cites work: New Hermite-Jensen-Mercer-type inequalities via \(k\)-fractional integrals
cites work: Hermite-Jensen-Mercer type inequalities for conformable integrals and related results
cites work: Popoviciu type inequalities for n-convex functions via extension of Montgomery identity
cites work: Q5615493
cites work: Convex functions, partial orderings, and statistical applications
cites work: On an Inequality for Convex Functions
cites work: On Jessen's inequality for convex functions
cites work: Some inequalities for starshaped and convex functions
cites work: Q3947856
cites work: Über eine Verallgemeinerung des Dirichletschen Integrals
cites work: Q5287501
cites work: Q5539510
cites work: Estimations of \(f\)- and Rényi divergences by using a cyclic refinement of the Jensen's inequality
cites work: Q5529067
cites work: Q4486979
cites work: Some properties of Zipf-Mandelbrot law and Hurwitz ζ-function
cites work: Zipf's law, power laws and maximum entropy
cites work: Hybrid Zipf-Mandelbrot law
description: scientific article; zbMATH DE number 7369041