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Simpson type inequalities and applications


Awan, Muhammad Uzair; Javed, Muhammad Zakria; Rassias, Michael Th; Noor, Muhammad Aslam; Noor, Khalida Inayat (2021). Simpson type inequalities and applications. Journal of Analysis, 29(4):1403-1419.

Abstract

A new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of \sigma >0. We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

Abstract

A new generalized integral identity involving first order differentiable functions is obtained. Using this identity as an auxiliary result, we then obtain some new refinements of Simpson type inequalities using a new class called as strongly (s, m)-convex functions of higher order of \sigma >0. We also discuss some interesting applications of the obtained results in the theory of means. In last we present applications of the obtained results in obtaining Simpson-like quadrature formula.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Algebra and Number Theory
Physical Sciences > Analysis
Physical Sciences > Applied Mathematics
Physical Sciences > Geometry and Topology
Uncontrolled Keywords:Applied Mathematics, Geometry and Topology, Algebra and Number Theory, Analysis
Language:English
Date:1 December 2021
Deposited On:13 Oct 2022 15:00
Last Modified:27 Apr 2024 01:40
Publisher:Springer
ISSN:2367-2501
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s41478-021-00319-4
Project Information:
  • : FunderUniversität Zürich
  • : Grant ID
  • : Project Title
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)