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Jensen–Mercer Inequality And Related Results In The Fractal Sense 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)

  • HIJAZ AHMAD

    (Section of Mathematics, International Telematic University, Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy3Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Thi-Qar 64001, Iraq)

  • TAHER A. NOFAL

    (Department of Mathematics, College of Science Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia)

Abstract

The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen–Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. The purpose of this paper is to establish a generalized Jensen–Mercer inequality for a generalized convex function on a real linear fractal set ℠α (0 < α ≤ 1). Further, we also demonstrate some generalized Jensen–Mercer-type inequalities by employing local fractional calculus. Lastly, some applications related to Jensen–Mercer inequality and α-type special means are given. The present approach is efficient, reliable, and may motivate further research in this area.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:01:n:s0218348x22400084
    DOI: 10.1142/S0218348X22400084
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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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