A STUDY OF FRACTIONAL HERMITE–HADAMARD–MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS

Thanin Sitthiwirattham (), Miguel Vivas-Cortez, Muhammad Aamir Ali (), HÃœSEYIN Budak () and Ä°brahim Avci ()
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Thanin Sitthiwirattham: Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
Miguel Vivas-Cortez: School of Physical and Mathematical Sciences, Faculty of Exact and Natural Sciences, Pontifical Catholic University of Ecuador, Av. 12 October 1076, Section, Quito 17-01-2184, Ecuador
Muhammad Aamir Ali: Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, P. R. China
HÜSEYIN Budak: Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Ä°brahim Avci: Department of Computer Engineering, Faculty of Engineering, Final International University, Kyrenia, Northern Cyprus, via Mersin 10, Turkey

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-13

Abstract: In this work, we prove a parameterized fractional integral identity involving differentiable functions. Then, we use the newly established identity to establish some new parameterized fractional Hermite–Hadamard–Mercer-type inequalities for differentiable function. The main benefit of the newly established inequalities is that these inequalities can be converted into some new Mercer inequalities of midpoint type, trapezoidal type, and Simpson’s type for differentiable functions. Finally, we show the validation of the results with the help of some mathematical examples and their graphs.

Keywords: Midpoint Inequalities; Trapezoidal Inequalities; Simpson’s Inequalities; Jensen–Mercer Inequality (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400164

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