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An Improvement Of Hã–Lder Integral Inequality On Fractal Sets And Some Related Simpson-Like Inequalities

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  • CHUNYAN LUO

    (Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

  • YUPING YU

    (Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

  • TINGSONG DU

    (Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China)

Abstract

The purpose of this work is to investigate some inequalities for generalized s-convexity on fractal sets ℠α, which are associated with Simpson-like inequalities. To this end, an improved version of Hölder inequality and a Simpson-like identity on fractal sets are established, in view of which we give several estimation-type results involving Simpson-like inequalities for the first-order differentiable mappings. Moreover, we provide five examples to illustrate our results. As applications with respect to local fractional integrals, we derive two inequalities according to α-type special means and generalized probability density functions.

Suggested Citation

  • Chunyan Luo & Yuping Yu & Tingsong Du, 2021. "An Improvement Of Hã–Lder Integral Inequality On Fractal Sets And Some Related Simpson-Like Inequalities," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-20, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21501267
    DOI: 10.1142/S0218348X21501267
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    Citations

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    Cited by:

    1. 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).
    2. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Yu, Yuping & Liu, Jun & Du, Tingsong, 2022. "Certain error bounds on the parameterized integral inequalities in the sense of fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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