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Sandwich theorem for reciprocally strongly convex functions

Abstract:

We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval (Formula Presented). iff there exists a reciprocally strongly convex function h : [a, b] → R such that f (x) ≤ h (x) ≤ g (x) for all x ∈ [a, b]. Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.