New extensions of Hermite-Hadamard and Fejér type inequalities using fuzzy fractional integral operators through different fuzzy convexities

Volume 40, Issue 4, pp 456--480 https://dx.doi.org/10.22436/jmcs.040.04.02

Publication Date: July 29, 2025 Submission Date: March 20, 2025 Revision Date: April 06, 2025 Accteptance Date: April 20, 2025

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Authors

R. S. Ali - Department of Mathematics and Statistics, the University of Lahore, Sargodha campus, Sargodha, Pakistan. M. Vivas-Cortez - FRACTAL (Fractional Research Analysis Convexity and Their Applications Laboratory), Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Ecuador. A. Kashuri - Department of Mathematical Engineering, Polytechnic University of Tirana, 1001 Tirana, Albania. N. Talib - Department of Mathematics and Statistics, the University of Lahore, Sargodha campus, Sargodha, Pakistan.

Abstract

It is a familiar fact to develop inequalities using the popular method by adopting fractional operators, and such study of methods is the main core of modern research in recent year. Fuzzy interval valued (FIV) mappings not only used to generalize of different convex mappings but also developed fractional operators. In this paper, we investigate fuzzy fractional inequalities for different fuzzy convexities by successfully implementing generalized fuzzy fractional operators (G-FFO). We discuss the extension of Hermite--Hadamard, trapezoid-type inequalities on the basis of fuzzy convexities and fuzzy fractional operators. Moreover, we establish the Fejér and midpoint type fuzzy inequalities for \((\eta_{1}, \eta_{2})\)-convex fuzzy function.

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Keywords

• Hermite-Hadamard type fuzzy inequality
• Fejér type fuzzy inequality
• generalized fuzzy fractional operators
• convex fuzzy interval valued function
• \((\eta_{1}, \eta_{2})\)-convex fuzzy interval valued function

MSC

•  26D07
•  26D10
•  26D15
•  26B25
•  26A33

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