Some ( p, q )-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

Humaira Kalsoom, Muhammad Amer, Moin-ud-Din Junjua, Sabir Hussain and Gullnaz Shahzadi
Additional contact information
Humaira Kalsoom: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
Muhammad Amer: Department of Basic Sciences, Deanship of Preparatory Year Program, University of Hail, Hail 2440, Saudi Arabia
Moin-ud-Din Junjua: Department of Mathematics and Statistics, Institute of Southern Punjab, Multan 32100, Pakistan
Sabir Hussain: Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
Gullnaz Shahzadi: Department of Mechanical Engineering, Ecole de Technologie Superieure, 1100 Notre-Dame W, Montreal, QC H3C 1K3, Canada

Mathematics, 2019, vol. 7, issue 8, 1-22

Abstract: In this paper, we present the preliminaries of ( p , q ) -calculus for functions of two variables. Furthermore, we prove some new Hermite-Hadamard integral-type inequalities for convex functions on coordinates over [ a , b ] × [ c , d ] by using the ( p , q ) -calculus of the functions of two variables. Furthermore, we establish an identity for the right-hand side of the Hermite-Hadamard-type inequalities on coordinates that is proven by using the ( p , q ) -calculus of the functions of two variables. Finally, we use the new identity to prove some trapezoidal-type inequalities with the assumptions of convexity and quasi-convexity on coordinates of the absolute values of the partial derivatives defined in the ( p , q ) -calculus of the functions of two variables.

Keywords: Hermite-Hadamard inequality; ( p , q )-calculus of functions of two variables; partial derivatives in ( p , q )-calculus of the functions of two variables; multiple integrals in ( p , q )-calculus of the functions of two variables; Hölder’s inequality in ( p , q )-calculus of the functions of two variables; coordinated convexity; coordinated quasi-convexity inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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