Hermite-Hadamard inequalities for generalized (m − F)-convex function in the framework of local fractional integrals

Arslan Razzaq, Iram Javed, Juan E. Nápoles V., Francisco Martínez González

Abstract


This work presents new versions of the Hermite-Hadamard Inequality, for (m−F)-convex functions, defined on fractal sets Rς ( 0 < ς ≤ 1). So, we show some new results for twice differentiable functions using local fractional calculus, as well as some new definitions. We will construct these new integral inequality using the generalized H¨older-integral inequality and the power mean integral inequality. Furthermore, we present some new inequalities for the midpoint and trapezoid formulas in a novel type of fractal calculus. The conclusions in this paper are substantial advancements and generalizations of prior research reported in the literature.


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References


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DOI: https://doi.org/10.52846/ami.v51i1.1775