On $\phi$-convexity

Abstract

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