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Generalizations of some Hermite-Hadamard-Fejér type inequalities for \(p\)-convex functions via generalized fractional integrals. (English) Zbl 1488.26097

Summary: In this paper firstly we obtain a version of the Hermite-Hadamard-Fejér inequality for \(p\)-convex functions via generalized fractional integral operator. Secondly we construct an integral identity and some Hermite-Hadamard-Fejér type integral inequalities for \(p\)-convex functions via generalized fractional integral operator. Being generalizations, we also deduce some known results.

MSC:

26D15 Inequalities for sums, series and integrals
26A33 Fractional derivatives and integrals
26A51 Convexity of real functions in one variable, generalizations
33E12 Mittag-Leffler functions and generalizations