Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain

摘要

The conception of extended fractal left-as well as right-side integral operators and the related Hermite- Hadamard's integral inequalities along with midpoint are proposed firstly in this paper. A midpoint-type integral identity in fractal domain, involving twice differentiable mappings, is then derived based on the introduced extended fractal integral operators for the objective of deriving fractal midpoint-type integral inequalities with the mappings whose second-order derivatives in absolute value are required to be generalized convex. Finally, a series of fractal outcomes regarding ??????-type special means, moments of random variable and wave equations are acquired as applications, correspondingly.

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