  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.
