Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Xuexiao You, Muhammad Aamir Ali, Hüseyin Budak, Jiraporn Reunsumrit and Thanin Sitthiwirattham
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Xuexiao You: School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Hüseyin Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey
Jiraporn Reunsumrit: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Thanin Sitthiwirattham: Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Mathematics, 2021, vol. 9, issue 20, 1-11

Abstract: In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.

Keywords: Hermite–Hadamard–Mercer inequality; Jensen inequality; harmonically convex function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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