Browsing by Author "Xuexiao You"

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    HermiteÐhadamardÐmercer-type inequalities for harmonically convex mappings
    (MDPI, 2021) Xuexiao You; Muhammad Aamir Ali; HŸseyin Budak; Jiraporn Reunsumrit; Thanin Sitthiwirattham; M.A. Ali; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China; email: mahr.muhammad.aamir@gmail.com; T. Sitthiwirattham; Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand; email: thanin_sit@dusit.ac.th
    In this paper, we prove HermiteÐHadamardÐMercer inequalities, which is a new version of the HermiteÐHadamard inequalities for harmonically convex functions. We also prove HermiteÐ HadamardÐMercer-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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.