Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

Volume 33, Issue 4, pp 352--367 https://dx.doi.org/10.22436/jmcs.033.04.03

Publication Date: January 25, 2024 Submission Date: October 26, 2023 Revision Date: December 04, 2023 Accteptance Date: December 19, 2023

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Authors

H. Ahmad - Near East University, Operational Research Center in Healthcare, TRNC Mersin 10, Nicosia, 99138, Turkey. - Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, 42210 , Saudi Arabia. - Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait. - Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. J. Nasir - Department of Mathematics , Virtual University of Pakistan, Lahore Campus, 54000, Pakistan. M. Tariq - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. M. Suleman - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. S. K. Ntouyas - Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece. J. Tariboon - Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.

Abstract

In this paper, we aim to discuss some fractional Hermite--Hadamard (H--H)-Mercer inequality for interval-valued functions via generalized fractional integral operator (GFIO). In addition, we investigate some new variants of the H--H-Mercer inequality pertaining to GFIO. A few examples are also provided to back up our claims. The findings potentially shed fresh light on a wide range of integral inequalities for fractional fuzzy in the frame of interval analysis and the optimization challenges they present. Finally, applications involving matrices are demonstrated.

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Keywords

• Convex function
• H--H-Mercer inequality
• interval-valued function
• generalized fractional integral operator

MSC

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15

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