Abdurrahman Gözpınar

Generalized Hermite-Hadamard type inequalities involving fractional integral operators

In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral.

Some new inequalities involving generalized fractional integral operators for several class of functions

In the present paper, several interesting integral inequalities involving fractional integral operators for different class of convex mappings are established. Our results in a special case yield results obtained by via Riemann-Liouville fractional integrals. Therefore, the results presented here would provide extensions of those given in earlier works.

Hermite-Hadamard type inequalities for the generalized k -fractional integral operators

We firstly give a modification of the known Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. We secondly establish several Hermite-Hadamard type inequalities for the generalized k-fractional integral operators of a function with respect to another function. The results presented here, being very general, are pointed out to be specialized to yield some known results. Relevant connections of the various results presented here with those involving relatively simple fractional integral operators are also indicated.

Hermite-Hadamard type inequalities for quasi-convex functions via new fractional conformable integrals

The main issue addressed in this paper is to prove generalization of Hermite-Hadamard type inequalities for quasi-convex functions via “new fractional conformable integrals” defined by Jarad et. al. [6]. The relevant connections of some results presented here with those earlier ones are also pointed out.

Hermite-Hadamard Type Inequalities for convex functions via generalized fractional integral operators

Abstract In this present work, the authors establish a new integral identity involving generalized fractional integral operators and by using this fractional-type integral identity, obtain some new Hermite-Hadamard type inequalities for functions whose first derivatives in absolute value are convex. Relevant connections of the results presented here with those earlier ones are also pointed out.

Some inequalities for generalized s-convex functions in the second sense on fractal sets

In this present paper, some new generalized Hermite-Hadamard type inequalities for functions whose second derivatives in absolute value are generalized s-convex in the second sense are obtained.