SOME HERMITE-HADAMARD INEQUALITIES INVOLVING WEIGHTED INTEGRAL OPERATORS VIA (h; s;m)-CONVEX FUNCTIONS

SOME HERMITE-HADAMARD INEQUALITIES INVOLVING WEIGHTED INTEGRAL OPERATORS VIA (h; s;m)-CONVEX FUNCTIONS

P. Korus, J. E. Napoles Valdes

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Abstract

In this work, we establish new integral inequalities of Hermite{Hadamard type, within the framework of generalized integrals, which contain the Riemann{Liouville fractional integrals as particular case. We use a de nition of convexity that includes the classical convex, m-convex, s-convex functions, among others. We show that several known results from the literature are closely related to ours.

Keywords

Hermite{Hadamard integral inequality, generalized integral operators, (h; s;m)- convex functions.