New fractional integral inequalities pertaining 2D–approximately coordinate (r1,ℏ1)-(r2,ℏ2)–convex functions

Abstract

In this article the authors introduce the concept of two dimensional approximately coordinate (r1,ℏ1)–(r2,ℏ2)–convex function that generalize several known coordinate convexity classes. Some refinements of Hermite–Hadamard like inequalities pertaining approximately coordinate (r1,ℏ1)–(r2,ℏ2)–convex functions are obtain and several special cases from the main results are discussed in details. Finally, from our main results some known results are recaptured as well.

Keywords

• Hermite–Hadamard inequality
• Hölder inequality
• Katugampola fractional integrals
• Convexity