New generalizations of Németh-Mohapatra type inequalities on time scales
type: Item
instance of: scholarly article
title: New generalizations of Németh-Mohapatra type inequalities on time scales
zbMATH Open document ID: 1399.26040
author: Xianqiang Yang
published in: Acta Mathematica Hungarica
publication date: 2018-04-12T00:00:00Z
review text: In recent papers, some classical inequalities have been extended to functions defined on time scales, that are closed subsets \(\mathbb T\) of \(\mathbb R\). Examples are \(\mathbb R\), \(\mathbb N\) when we obtain the classical integral and discrete versions; but there are others in use such as \(\{q^t: t\in \mathbb N_0, q>1\}\); see \textit{M. Bohner} and \textit{A. Peterson} [Dynamic equations on time scales. An introduction with applications. Basel: Birkhäuser (2001; Zbl 0978.39001)]. In this paper, time scale versions of the discrete inequalities of \textit{J. Németh} [Acta Sci. Math. 32, 295--299 (1971; Zbl 0226.26020)] and the analogous integral inequalities of \textit{R. N. Mohapatra} and \textit{D. C. Russell} [Aequationes Math. 28, 199--207 (1985; Zbl 0573.26010)] are proved. The results are used to obtain new generalisations of several classical inequalities.
reviewed by: P. S. Bullen
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 34A40
Mathematics Subject Classification ID: 34N05
zbMATH DE Number: 6859253
zbMATH Keywords: Németh-Mohapatra inequality
zbMATH Keywords: Copson inequality
zbMATH Keywords: Besseck inequality
zbMATH Keywords: Hardy inequality
zbMATH Keywords: time scale
MaRDI profile type: Publication
full work available at URL: s10474-017-0718-2
OpenAlex ID: W2606773936
cites work: SOME ELEMENTARY INEQUALITIES
cites work: Minkowski and Beckenbach-Dresher inequalities and functionals on time scales
cites work: Q2723195
cites work: Q4797834
cites work: 13.—Some Integral Inequalities
cites work: Extensions of Copson's inequalities
cites work: On Hardy's inequality and its generalization
cites work: Q4784073
cites work: Q5439977
cites work: Q5601561
cites work: Integral inequalities related to Hardy's inequality
cites work: Q5632833
cites work: Q3997067
cites work: Time scales Hardy-type inequalities via superquadracity
cites work: Time scale Hardy-Knopp type integral inequalities
cites work: Hardy inequality on time scales and its application to half-linear dynamic equations
cites work: A new class of dynamic inequalities of Hardy's type on time scales
cites work: Dynamic inequalities of Hardy and Copson type on time scales
cites work: Generalized Hardy, Copson, Leindler and Bennett inequalities on time scales
cites work: Some dynamic inequalities of Hardy type on time scales
cites work: Weighted Hardy-type inequalities on time scales with applications
DOI: 10.1007/S10474-017-0718-2
description: scientific article; zbMATH DE number 6859253