General Trapezoidal-Type Inequalities in Fuzzy Settings

Muhammad Amer Latif ()
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Muhammad Amer Latif: Department of Mathematics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia

Mathematics, 2024, vol. 12, issue 19, 1-23

Abstract: In this study, trapezoidal-type inequalities in fuzzy settings have been investigated. The theory of fuzzy analysis has been discussed in detail. The integration by parts formula of analysis of fuzzy mathematics has been employed to establish an equality. Trapezoidal-type inequality for functions with values in the fuzzy number-valued space is proven by applying the proven equality together with the properties of a metric defined on the set of fuzzy number-valued space and Höler’s inequality. The results proved in this research provide generalizations of the results from earlier existing results in the field of mathematical inequalities. An example is designed by defining a function that has values in fuzzy number-valued space and validated the results numerically using the software Mathematica (latest v. 14.1). The p -levels of the defined fuzzy number-valued mapping have been shown graphically for different values of p ∈ 0 , 1 .

Keywords: trapezoidal inequality; fuzzy real number; fuzzy trapezoidal-type inequality; Banach spaces; gH -differentiable function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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