In this paper, we introduce the notion of exponentially p-convex function and exponentially s-convex function in the second sense. We establish several Hermite-Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in second sense. The present investigation is an extension of several well known results.
In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generalization of Riemann–Liouville fractional integral and Hadamard fractional integral. We show that through the Katugampola fractional integral we can find a Hermite–Hadamard inequality via the Riemann–Liouville fractional integral.
In this paper, we obtained the Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for p-convex functions via new fractional conformable integral operators. We also gave some new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for convex functions and harmonically convex functions via new fractional conformable integral operators.
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