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DISCRETE HERMITE–HADAMARD-TYPE INEQUALITIES FOR (s,m)-CONVEX FUNCTION

Author

Listed:
  • YONGFANG QI

    (Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China)

  • QINGZHI WEN

    (Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China)

  • GUOPING LI

    (��Scientific Research Planning Division, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China)

  • KECHENG XIAO

    (Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China)

  • SHAN WANG

    (Department of Mathematics, Pingxiang University, Pingxiang, Jiangxi 337055, P. R. China)

Abstract

The Hermite–Hadamard (HH)-type inequality plays a very important role in the fields of basic mathematics and applied mathematics. In recent years, many scholars have expanded and improved it. Although we have achieved some research results about HH-type inequality, the research on discrete HH-type inequalities has just begun, and a lot of work needs to be improved. In this paper, we introduce (s,m)-convex function and present discrete HH-type inequalities on time scale with discrete substitution method. In addition, the Hermite–Hadamard–Fejér(HHF)-type inequalities on time scale will be obtained, where the integrand is ϕφ, ϕ is (s,m)-convex function on [a,b] and φ is symmetric with respect to a+mb 2, our results in some special cases yield the well-known classic HHF-type inequalities. Finally, through the discrete substitution method, we get discrete fractional HH-type inequality and discrete fractional HHF-type inequality for (s,m)-convex function.

Suggested Citation

  • Yongfang Qi & Qingzhi Wen & Guoping Li & Kecheng Xiao & Shan Wang, 2022. "DISCRETE HERMITE–HADAMARD-TYPE INEQUALITIES FOR (s,m)-CONVEX FUNCTION," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-10, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501602
    DOI: 10.1142/S0218348X22501602
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    Cited by:

    1. Khan, Muhammad Bilal & Othman, Hakeem A. & Santos-García, Gustavo & Saeed, Tareq & Soliman, Mohamed S., 2023. "On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued mappings," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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