A note on generalized convex functions

Abstract

Abstract In the article, we provide an example for a η-convex function defined on rectangle is not convex, prove that every η-convex function defined on rectangle is coordinate η-convex and its converse is not true in general, define the coordinate (η1,η2) $(\eta _{1}, \eta _{2})$-convex function and establish its Hermite–Hadamard type inequality.

Keywords

• Convex function
• Coordinate convex function
• η-convex function
• Coordinate ( η 1 , η 2 ) $(\eta _{1}, \eta _{2})$ -convex function