Abstract
Convexity is crucial in obtaining many forms of inequalities. As a result, there is a significant link between convexity and integral inequality. Due to the significance of these concepts, the purpose of this study is to introduce a new class of generalized convex interval-valued functions called (p,s)-convex fuzzy interval-valued functions ((p,s)-convex F-I-V-Fs) in the second sense and to establish Hermite–Hadamard (H–H) type inequalities for (p,s)-convex F-I-V-Fs using fuzzy order relation. In addition, we demonstrate that our results include a large class of new and known inequalities for (p,s)-convex F-I-V-Fs and their variant forms as special instances. Furthermore, we give useful examples that demonstrate usefulness of the theory produced in this study. These findings and diverse approaches may pave the way for future research in fuzzy optimization, modeling, and interval-valued functions.
Highlights
A convex function has a convex set as its epigraph; the theory of inequality of convex functions falls under the umbrella of convexity
Many contemporary difficulties in economics and engineering, the relevance of convex analysis is well recognized in optimization theory [1,2,3], and the idea of convexity no longer suffices
F-I-V-Fs over is denoted by t,over s(R)
Summary
A convex function has a convex set as its epigraph; the theory of inequality of convex functions falls under the umbrella of convexity. It is a significant theory in and of itself, as it affects practically all fields of mathematics. The graphical analysis is most often the initial issue that necessitates the acquaintance with this theory. This is an opportunity to learn about the second derivative test of convexity, which is a useful tool for detecting convexity. Many contemporary difficulties in economics and engineering, the relevance of convex analysis is well recognized in optimization theory [1,2,3], and the idea of convexity no longer suffices
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