p-convex function

In this paper, we establish extensions of Jensen’s discrete inequality for the class of p-convex functions. Also, we give lower and upper bounds for this inequality. We apply these results in information theory and obtain new and strong bounds for Shannon’s entropy of a probability distribution. Also, We give some applications.

Here our aim is to prove the Hermite-Hadamard and Fejér inequalities for p-convex functions via Caputo fractional derivatives. We also establish some useful identities in order to find further Hadamard’s and Fejér type inequalities which are generalizations of the results given in the literature cited here.