On a generalization of the Opial inequality
type: Item
instance of: scholarly article
title: On a generalization of the Opial inequality
author: Paul Bosch
author: Ana Portilla
author: José M. Rodríguez
author: Jose M. Sigarreta
published in: Demonstratio Mathematica
publication date: 2024-06-11T00:00:00Z
review text: \textit{Z. Opial} [Ann. Pol. Math. 9, 145--155 (1960; Zbl 0098.29102)] stated and proved the following classical inequality\N\[\N\int^h_0\mid f(x)f'(x)\mid dx\le\frac1{4}\int^h_0\mid f'(x)\mid^2dx,\N\]\Nwhere \(f\in C^1[0,h]\) and satisfies \(f(0)=f(h)=0\) and \(f(x) >0\) for all \(x\in (0,h)\). The above inequality is referred to as Opial's inequality. In this paper, the authors derive and prove some new Opial-type inequalities and give applications to the generalized Riemann-Liouville-type integral operators. The key results of the paper are given in Theorems 1 and 3 and several consequences of their results are pointed out and well discussed.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7863324
zbMATH Keywords: fractional derivatives and integrals
zbMATH Keywords: fractional integral inequalities
zbMATH Keywords: Opial-type inequalities
MaRDI profile type: Publication
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DOI: 10.1515/DEMA-2023-0149
description: scientific article; zbMATH DE number 7863324