Some Ostrowski type inequalities for mappings whose second derivatives are preinvex function via fractional integral operator

Abstract

The comprehension of inequalities in preinvexity is very important for studying fractional calculus and its effectiveness in many applied sciences. In this article, we develop and study of fractional integral inequalities whose second derivatives are preinvex functions. We investigate and prove new lemma for twice differentiable functions involving Riemann-Liouville(R-L) fractional integral operator. On the basis of this newly developed lemma, we make some new results regarding of this identity. These new results yield us some generalizations of the prior results. This study builds upon on a novel new auxiliary result which enables us to develop new variants of Ostrowski type inequalities for twice differentiable preinvex mappings. As an application, several estimates concerning Bessel functions of real numbers are also illustrated.

Keywords

• convex function
• hermite-hadamard inequality
• hölder inequality
• power mean inequality
• young's inequality
• hölder-i̇şcan
• improved power means inequality
• riemann-liouville fractional integral operator