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Certain error bounds on the parameterized integral inequalities in the sense of fractal sets

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  • Yu, Yuping
  • Liu, Jun
  • Du, Tingsong

Abstract

The objective of this study is to research certain integral inequalities with a parameter through the generalized (s, P)-preinvex mappings in the frame of fractal space. In view of this, we propose and investigate the conception of the generalized (s, P)-preinvex mappings and their related properties. Meanwhile, we establish an integral identity in the settings of fractal sets and present the parameterized integral inequalities for mappings whose first-order derivatives in absolute value belong to the generalized (s, P)-preinvexity. As applications with regard to local fractional integral operators, we consider applying the derived findings to v-type special means, numerical integrations, as well as extended probability distribution mappings, respectively.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005380
    DOI: 10.1016/j.chaos.2022.112328
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    References listed on IDEAS

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    5. Wenbing Sun, 2021. "LOCAL FRACTIONAL OSTROWSKI-TYPE INEQUALITIES INVOLVING GENERALIZED h-CONVEX FUNCTIONS AND SOME APPLICATIONS FOR GENERALIZED MOMENTS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-12, February.
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    7. Wenbing Sun, 2021. "HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED s-PREINVEX FUNCTIONS AND THEIR GENERALIZATION," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(04), pages 1-16, June.
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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).
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    3. Abdullah Ali H. Ahmadini & Waqar Afzal & Mujahid Abbas & Elkhateeb S. Aly, 2024. "Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1 , h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems," Mathematics, MDPI, vol. 12(3), pages 1-28, January.

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