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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.

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  • 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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    3. 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.
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    6. 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.
    4. Çi̇ri̇ş, Sümeyye Ermeydan & Yildirim, Hüseyin, 2024. "Hermite–Hadamard inequalities for generalized σ−conformable integrals generated by co-ordinated functions," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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