Remarks on strongly convex functions
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Some properties of strongly convex functions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers–Ulam stability result for strongly convex functions are given. An integral Jensen-type inequality and a Hermite–Hadamard-type inequality for strongly convex functions are obtained. Finally, a relationship between strong convexity and generalized convexity in the sense of Beckenbach is shown.
Mathematics Subject Classification (2000)Primary 26A51 Secondary 39B62
KeywordsStrongly convex functions generalized convex functions Jensen inequality Hermite–Hadamard inequality
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