In what follows, a hierarchy of m -convexity is considered: we define m -starshaped functions, m -superadditive functions, Jensen m -convex functions, weak Jensen m -convex functions, Jensen m -superadditive functions, and weak m -superadditive functions. Some inclusions between such classes of functions are established. We also analyze the validity of the Hermite-Hadamard inequality, and of the Chebyshev-Andersson inequality for m -convex functions.
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Gheorghe Toader (2009) studied this question.
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