Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae

Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae

In this article, we develop a new class of trapezium-type inequalities up to twice differentiable h-convex mappings for fractional integrals of Riemann-type. We conclude numerous existing results in literature from our general inequalities. Based on our consequences, we will obtain some quadrature f...

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Main Authors: Muhammad Samraiz, Fakhra Nawaz, Bahaaeldin Abdalla, Thabet Abdeljawad, Gauhar Rahman, Sajid Iqbal
Format: Article
Language:English
Published: AIMS Press 2021-05-01
Series:AIMS Mathematics
Subjects:
mid-point type inequalities
generalized riemann-liouville fractional integral operator
h-convex
s-convex
Online Access:https://www.aimspress.com/article/doi/10.3934/math.2021443?viewType=HTML
id doaj-0c9539d7cc4445b39c7825c0c16d9cd1
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spelling doaj-0c9539d7cc4445b39c7825c0c16d9cd12021-05-26T02:04:30ZengAIMS PressAIMS Mathematics2473-69882021-05-01677625764810.3934/math.2021443Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulaeMuhammad Samraiz0Fakhra Nawaz1Bahaaeldin Abdalla 2Thabet Abdeljawad3Gauhar Rahman4Sajid Iqbal51. Department of Mathematics, University of Sargodha, Sargodha, Pakistan1. Department of Mathematics, University of Sargodha, Sargodha, Pakistan2. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 12345, Saudi Arabia2. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 12345, Saudi Arabia 3. Department of Medical Research, China Medical University, Taichung 40402, Taiwan 4. Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan5. Department of Mathematics and Statistics, Hazara University Mansehra, Pakistan6. Department of Mathematics, Ripha International University, Faisalabad Campus, Satyana Road, 38000 Faisalabad, PakistanIn this article, we develop a new class of trapezium-type inequalities up to twice differentiable h-convex mappings for fractional integrals of Riemann-type. We conclude numerous existing results in literature from our general inequalities. Based on our consequences, we will obtain some quadrature formulas as applications.https://www.aimspress.com/article/doi/10.3934/math.2021443?viewType=HTMLmid-point type inequalitiesgeneralized riemann-liouville fractional integral operatorh-convexs-convex
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Samraiz
Fakhra Nawaz
Bahaaeldin Abdalla
Thabet Abdeljawad
Gauhar Rahman
Sajid Iqbal
spellingShingle Muhammad Samraiz
Fakhra Nawaz
Bahaaeldin Abdalla
Thabet Abdeljawad
Gauhar Rahman
Sajid Iqbal
Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
AIMS Mathematics
mid-point type inequalities
generalized riemann-liouville fractional integral operator
h-convex
s-convex
author_facet Muhammad Samraiz
Fakhra Nawaz
Bahaaeldin Abdalla
Thabet Abdeljawad
Gauhar Rahman
Sajid Iqbal
author_sort Muhammad Samraiz
title Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
title_short Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
title_full Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
title_fullStr Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
title_full_unstemmed Estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
title_sort estimates of trapezium-type inequalities for h-convex functions with applications to quadrature formulae
publisher AIMS Press
series AIMS Mathematics
issn 2473-6988
publishDate 2021-05-01
description In this article, we develop a new class of trapezium-type inequalities up to twice differentiable h-convex mappings for fractional integrals of Riemann-type. We conclude numerous existing results in literature from our general inequalities. Based on our consequences, we will obtain some quadrature formulas as applications.
topic mid-point type inequalities
generalized riemann-liouville fractional integral operator
h-convex
s-convex
url https://www.aimspress.com/article/doi/10.3934/math.2021443?viewType=HTML
work_keys_str_mv AT muhammadsamraiz estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
AT fakhranawaz estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
AT bahaaeldinabdalla estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
AT thabetabdeljawad estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
AT gauharrahman estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
AT sajidiqbal estimatesoftrapeziumtypeinequalitiesforhconvexfunctionswithapplicationstoquadratureformulae
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