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

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  • Yu, Shuhong
  • Zhou, Yunxiu
  • Du, Tingsong

Abstract

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 ɛ-type special means, moments of random variable and wave equations are acquired as applications, correspondingly.

Suggested Citation

  • Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008402
    DOI: 10.1016/j.chaos.2022.112661
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