Rad HAZU, Matematičke znanosti, Vol. 29 (2025), 187-205.

THE HERMITE-HADAMARD INEQUALITY FOR MφMψ-h-CONVEX FUNCTIONS AND RELATED INTERPOLATIONS

Sanja Varošanec

University of Zagreb, Faculty of Science, Department of Mathematics, Bijenička 30, 10000 Zagreb, Croatia
e-mail: varosans@math.hr

Abstract.   In this paper we consider the Hermite-Hadamard inequality for MφMψ-h-convex functions. An MφMψ-h-convexity covers several particular types of generalized convexity such as a harmonic-h-convexity, a log-h-convexity, (h, p)-convexity, MpA-h-convexity, MφMψ-convexity etc. The Hermite-Hadamard type inequalities with two and with n nodes are given. Special attention is paid to a dyadic partition of an interval and related interpolations.

2020 Mathematics Subject Classification.   26A51, 26A15.

Key words and phrases.   Hermite-Hadamard inequality, MφMψ-h-convex function, quasi-arithmetic mean, dyadic partition.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/9e31lhzoqm

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