Abstract
In both theoretical and applied mathematics fields, integral inequalities play a critical role. Due to the behavior of the definition of convexity, both concepts convexity and integral inequality depend on each other. Therefore, the relationship between convexity and symmetry is strong. Whichever one we work on, we introduced the new class of generalized convex function is known as LR-left({h}_{1}, {h}_{2}right)-convex interval-valued function (LR-left({h}_{1}, {h}_{2}right)-IVF) by means of pseudo order relation. Then, we established its strong relationship between Hermite–Hadamard inequality (HH-inequality)) and their variant forms. Besides, we derive the Hermite–Hadamard–Fejér inequality (HH–Fejér inequality)) for LR-left({h}_{1}, {h}_{2}right)-convex interval-valued functions. Several exceptional cases are also obtained which can be viewed as its applications of this new concept of convexity. Useful examples are given that verify the validity of the theory established in this research. This paper’s concepts and techniques may be the starting point for further research in this field.
Highlights
The theory of convexity in pure and applied sciences has become a rich source of inspiration
Every function is convex function, if and only if it satisfies an integral inequality, which is known as HH-inequality
Inspired by Costa and Roman-Flores [8], and Zhang et al [27], we present interval inequality and interval HH–Fejér inequality for LR- h1, h2 -convex-IVFs by means of pseudo order relation
Summary
The theory of convexity in pure and applied sciences has become a rich source of inspiration. We urge the readers for further analysis of literature on the applications and properties of generalized convex functions and HH-integral inequalities, see [2, 3, 10, 12,13,14,15, 24] and the references therein. Since its inspection five decades ago, the theory of fuzzy sets and system has advanced in variety of ways, see [26] It plays an important role in the study of a broad-based class problems in pure mathematics and applied sciences including operational analysis, computer science, managements sciences, artificial intelligence, control engineering and decision-makings. The main purpose of this paper is to introduce a new class of LR- h1, h2 -convex-IVF and to develop a close relationship between Hermite–Hadamard type and Hermite–Hadamard–Fejér type inequalities for LR- h1, h2 -convex-IVF
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