Hermite–Hadamard and Pachpatte Type Inequalities for Coordinated Preinvex Fuzzy-Interval-Valued Functions Pertaining to a Fuzzy-Interval Double Integral Operator

Gustavo Santos-García, Muhammad Bilal Khan, Hleil Alrweili, Ahmad Aziz Alahmadi and Sherif S. M. Ghoneim
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Gustavo Santos-García: Facultad de Economía y Empresa, Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007 Salamanca, Spain
Muhammad Bilal Khan: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Hleil Alrweili: Department of Mathematics, Faculty of Art and Science, Northern Border University, Rafha, Saudi Arabia
Ahmad Aziz Alahmadi: Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Sherif S. M. Ghoneim: Department of Electrical Engineering, College of Engineering, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2022, vol. 10, issue 15, 1-25

Abstract: Many authors have recently examined the relationship between symmetry and generalized convexity. Generalized convexity and symmetry have become a new area of study in the field of inequalities as a result of this close relationship. In this article, we introduce the idea of preinvex fuzzy-interval-valued functions (preinvex F?I-V?F) on coordinates in a rectangle drawn on a plane and show that these functions have Hermite–Hadamard-type inclusions. We also develop Hermite–Hadamard-type inclusions for the combination of two coordinated preinvex functions with interval values. The weighted Hermite–Hadamard-type inclusions for products of coordinated convex interval-valued functions discussed in a recent publication by Khan et al. in 2022 served as the inspiration for our conclusions. Our proven results expand and generalize several previous findings made in the body of literature. Additionally, we offer appropriate examples to corroborate our theoretical main findings.

Keywords: fuzzy-interval-valued function; fuzzy-interval double integral operator; coordinated preinvex fuzzy-interval-valued function; Hermite–Hadamard inequality; Hermite–Hadamard–Fejér inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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