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An Improvement Of The Power-Mean Integral Inequality In The Frame Of Fractal Space And Certain Related Midpoint-Type Integral Inequalities

Author

Listed:
  • SHUHONG YU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • PSHTIWAN OTHMAN MOHAMMED

    (��Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Iraq)

  • LEI XU

    (Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China)

  • TINGSONG DU

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

Abstract

First, we construct a reformative version of the power-mean integral inequality in the sense of fractal space. Second, we define what we named as the generalized (s,P)-convex mappings, and investigate some related properties. Moreover, in accordance with the derived midpoint-type integral identities on fractal space, we establish certain improvements of the midpoint-type integral inequalities for mappings whose first-order derivatives in absolute value belong to the generalized (s,P)-convex mappings. As applications in association with local fractional calculus, we acquire three inequalities considering ν-type arithmetic mean and β-logarithmic mean, numerical integration, as well as probability density mappings, respectively.

Suggested Citation

  • Shuhong Yu & Pshtiwan Othman Mohammed & Lei Xu & Tingsong Du, 2022. "An Improvement Of The Power-Mean Integral Inequality In The Frame Of Fractal Space And Certain Related Midpoint-Type Integral Inequalities," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(04), pages 1-23, June.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:04:n:s0218348x22500852
    DOI: 10.1142/S0218348X22500852
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    Cited by:

    1. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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).

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