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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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    1. Huixia Mo & Xin Sui, 2014. "Generalized -Convex Functions on Fractal Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
    2. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, June.
    3. Luo, Chunyan & Wang, Hao & Du, Tingsong, 2020. "Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    4. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    5. Saad Ihsan Butt & Saba Yousaf & Hijaz Ahmad & Taher A. Nofal, 2022. "Jensen–Mercer Inequality And Related Results In The Fractal Sense With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-11, February.
    6. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    7. Pensri Pramukkul & Adam Svenkeson & Paolo Grigolini & Mauro Bologna & Bruce West, 2013. "Complexity and the Fractional Calculus," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-7, April.
    8. 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.
    9. Erden, Samet & Sarikaya, Mehmet Zeki, 2016. "Generalized Pompeiu type inequalities for local fractional integrals and its applications," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 282-291.
    10. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    11. Saad Ihsan Butt & Saba Yousaf & Muhammad Younas & Hijaz Ahmad & Shao-Wen Yao, 2022. "Fractal Hadamard–Mercer-Type Inequalities With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-14, March.
    12. A. Barani & S. Barani & S. S. Dragomir, 2012. "Refinements of Hermite-Hadamard Inequalities for Functions When a Power of the Absolute Value of the Second Derivative Is P -Convex," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, July.
    13. Butt, Saad Ihsan & Yousaf, Saba & Akdemir, Ahmet Ocak & Dokuyucu, Mustafa Ali, 2021. "New Hadamard-type integral inequalities via a general form of fractional integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    14. Ahmet Ocak Akdemir & Saad Ihsan Butt & Muhammad Nadeem & Maria Alessandra Ragusa, 2021. "New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
    15. Huixia Mo & Xin Sui & Dongyan Yu, 2014. "Generalized Convex Functions on Fractal Sets and Two Related Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
    16. 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.
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