pq-Simpson’s Type Inequalities Involving Generalized Convexity and Raina’s Function

Author:

Vivas-Cortez Miguel1ORCID,Baig Ghulam Murtaza2ORCID,Awan Muhammad Uzair3ORCID,Brahim Kamel4

Affiliation:

1. Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076, Quito 17-01-2184, Ecuador

2. Department of Mathematics, University of Management and Technology C-II, Lahore 54700, Pakistan

3. Department of Mathematics, Government College University, Faisalabad 38000, Pakistan

4. Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia

Abstract

This study uses Raina’s function to obtain a new coordinated pq-integral identity. Using this identity, we construct several new pq-Simpson’s type inequalities for generalized convex functions on coordinates. Setting p1=p2=1 in these inequalities yields well-known quantum Simpson’s type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks.

Funder

Pontificia Universidad Católica del Ecuador

Publisher

MDPI AG

Reference43 articles.

1. On Simpson’s inequality and applications;Dragomir;J. Inequal. Appl.,2000

2. Pečaric, J.E., Proschan, F., and Tong, Y.L. (1992). Convex Functions, Partial Orderings and Statistical Applications, Academic Press.

3. New inequalities of Simpson’s type for s-convex functions with applications;Alomari;RGMIA Res. Rep. Coll.,2009

4. On new inequalities of Simpson’s type for convex functions;Sarikaya;RGMIA Res. Rep. Coll.,2010

5. On generalizations of some inequalities for convex functions via quantum integrals;Erden;RACSAM,2020

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