The study presents clear definitions of w-convexity and integral forms of Hermite-Hadamard inequalities, suggesting wider applications in mathematical analysis.
In this work we present simple characterizations of W-convex and W-log-convex functions. As applications, we give short proofs for integral forms of Hermite-Hadamard or Levin-Steckin inequalities. We also give a characterization theorem for inner product spaces as normed spaces satisfying a certain property.
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Marinescu et al. (2025) studied this question.
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