On $\varphi$-convexity

Abstract

In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and $\varphi$-midconvex functions are obtained. Furthermore, the relationship between $\varphi$-midconvexity and $\varphi$-convexity is established.