Generalized Convexity and Related Integral Inequalities on Fractal Sets

Abstract

In this proposal we will present the generalized convexity and related integral inequali- ties on fractal sets Rϖ ( 0 < ϖ ≤ 1). Thus, these developments allow us to develop new bounds for integral inequalities. We will give generalized Hermite-Hadmard (H-H) type inequalities in fractal sense. In this research work we will present some new results by em- ploying local fractional calculus for twice differentiable functions and we will give some new applications along with some new definitions. For the development of these new in- tegral inequalities, we will use generalized H¨older-integral inequalities and Power mean integral inequalities by using local fractional calculus. We will give some new inequalities for midpoint and trapezoid formula for new class of local fractal calculus. Hence, these new results will lead us to generalization of prior results.