Some Hermite-Hadamard-Fejér Inequalities for ( η 1 , η 2 )-Convex Functions on the Coordinates

Abstract

This paper establishes new Hermite-Hadamard-Fejér type inequalities for functions that are ( η 1 , η 2 ) -convex on the coordinates. By employing weighted symmetric functions and generalized invexity, we derive several double integral inequalities that extend and unify classical results. These inequalities provide refined estimates that may be applied to error analysis in numerical integration and to bounding families of special functions, including Beta and hypergeometric functions. The results presented here demonstrate that the class of ( η 1 , η 2 ) -convex functions yields sharper bounds compared with conventional convexity and preinvex frameworks.