Bounds for the remainder in Simpson's inequality via \(n\)-polynomial convex functions of higher order using Katugampola fractional integrals
type: Item
instance of: scholarly article
title: Bounds for the remainder in Simpson's inequality via \(n\)-polynomial convex functions of higher order using Katugampola fractional integrals
zbMATH Open document ID: 1489.26020
DOI: 10.1155/2020/4189036
author: Yu-Ming Chu
author: Muhammad Uzair Awan
author: Muhammad Zakria Javad
author: Awais Gul Khan
published in: Journal of Mathematics
publication date: 2021-01-07T00:00:00Z
review text: Summary: The goal of this paper is to derive some new variants of Simpson's inequality using the class of \(n\)-polynomial convex functions of higher order. To obtain the main results of the paper, we first derive a new generalized fractional integral identity utilizing the concepts of Katugampola fractional integrals. This new fractional integral identity will serve as an auxiliary result in the development of the main results of this paper.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7290888
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/4189036
OpenAlex ID: W3080315892
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cites work: \(2D\) approximately reciprocal \(\rho\)-convex functions and associated integral inequalities
cites work: On Simpson's inequality and applications
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cites work: Conformable fractional integral inequalities for \(GG\)- and \(GA\)-convex functions
cites work: Delay dynamic double integral inequalities on time scales with applications
cites work: Generation of new fractional inequalities via \(n\) polynomials \(s\)-type convexity with applications
cites work: On Pólya-Szegö and Čebyšev type inequalities via generalized \(k\)-fractional integrals
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cites work: New approach to a generalized fractional integral
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description: scientific article; zbMATH DE number 7290888