TY - JOUR
T1 - A STUDY of FRACTIONAL HERMITE-HADAMARD-MERCER INEQUALITIES for DIFFERENTIABLE FUNCTIONS
AU - Sitthiwirattham, Thanin
AU - Vivas-Cortez, Miguel
AU - Ali, Muhammad Aamir
AU - Budak, Hüseyin
AU - Avci, Ibrahim
N1 - Publisher Copyright:
© The Author(s)
PY - 2024/1/18
Y1 - 2024/1/18
N2 - 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.
AB - 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.
KW - Jensen-Mercer Inequality
KW - Midpoint Inequalities
KW - Simpson's Inequalities
KW - Trapezoidal Inequalities
UR - http://www.scopus.com/inward/record.url?scp=85183563941&partnerID=8YFLogxK
U2 - 10.1142/S0218348X24400164
DO - 10.1142/S0218348X24400164
M3 - Article
AN - SCOPUS:85183563941
SN - 0218-348X
VL - 32
JO - Fractals
JF - Fractals
IS - 2
M1 - 2440016
ER -