Browsing by Author "Ibrahim Avci"

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    A STUDY OF FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS
    (World Scientific, 2024) Thanin Sitthiwirattham; Miguel Vivas-Cortez; Muhammad Aamir Ali; HŸseyin Budak; Ibrahim Avci; M. Vivas-Cortez; School of Physical and Mathematical Sciences, Faculty of Exact and Natural Sciences Pontifical Catholic, University of Ecuador, Quito, Av. 12 October 1076, Section, 17-01-2184, Ecuador; email: mjvivas@puce.edu.ec
    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. © The Author(s)