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

Yongfang Qi, Qingzhi Wen, Guoping Li, Kecheng Xiao and Shan Wang
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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

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-10

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.

Keywords: Hermite–Hadamard Inequality; Hermite–Hadamard–Fejér Inequality; (s; m)-Convex Function; Fractional Integrals; Time Scale (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501602

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