Generalized Hermite-Hadamard type inequalities for generalized F-convex function via local fractional integrals

In this paper, we will present the new generalized F-convexity and related integral inequalities on fractal sets R ������ (0 < ������& LE; 1). These developments allow us to develop new bounds for integral inequalities. We will give new generalized Hermite-Hadamard type inequalities in the fractals sense. In this work, we present some new results by employing local fractional calculus for twice differentiable functions along with some new definitions. For the development of these new integral inequalities, we will use generalized Hilder-integral inequality and power mean integral inequality by using local fractional calculus. Moreover, we give some new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus. The results raised in this paper provide significant extensions and generalizations of other related results given in earlier works.

Automated summary

In this paper, a new generalized F-convexity and related integral inequalities on fractal sets are presented. These developments result in new bounds for integral inequalities. New generalized Hermite-Hadamard type inequalities in the fractal sense are also introduced. The paper proposes new results by employing local fractional calculus and new definitions for twice differentiable functions. Additionally, new inequalities for midpoint and trapezoid formula for a new class of local fractional calculus are given.