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Fractal Hadamard–Mercer-Type Inequalities With Applications

Author

Listed:
  • SAAD IHSAN BUTT

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan)

  • SABA YOUSAF

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan)

  • MUHAMMAD YOUNAS

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan)

  • HIJAZ AHMAD

    (Information Technology Application and Research Center, Istanbul Ticaret University, 34445 Istanbul, Turkey3Department of Mathematics, Faculty of Humanities and Social Sciences, Istanbul Ticaret University, 34445 Istanbul, Turkey)

  • SHAO-WEN YAO

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China)

Abstract

Fractal analysis is a totally new area of research based on local fractional calculus. It has interesting applications in various fields such as a complex graph, computer graphics, the music industry, picture compression and many more fields. In this paper, we present new variants of Hadamard–Mercer-type inequalities on fractal sets ℠α (0 < α ≤ 1) by employing generalized convex function. We establish two new lemmas involving local fractional integrals. By using these lemmas, we obtain several results related to generalized Hadamard–Mercer-type integral inequalities for local differentiable generalized convex functions on real linear fractal space. Finally, we give applications for probability density functions and compute new generalized means.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:02:n:s0218348x22400552
    DOI: 10.1142/S0218348X22400552
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    Citations

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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).
    3. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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