On $φ$-convexity

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

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