Abstract
The concepts of convex and non-convex functions play a key role in the study of optimization. So, with the help of these ideas, some inequalities can also be established. Moreover, the principles of convexity and symmetry are inextricably linked. In the last two years, convexity and symmetry have emerged as a new field due to considerable association. In this paper, we study a new version of interval-valued functions (I-V·Fs), known as left and right χ-pre-invex interval-valued functions (LR-χ-pre-invex I-V·Fs). For this class of non-convex I-V·Fs, we derive numerous new dynamic inequalities interval Riemann–Liouville fractional integral operators. The applications of these repercussions are taken into account in a unique way. In addition, instructive instances are provided to aid our conclusions. Meanwhile, we’ll discuss a few specific examples that may be extrapolated from our primary findings.
Highlights
The Hermite–Hadamard inequality is a well-known inequality in convex function theory, with a geometrical explanation and a wide range of applications.Hermite–Hadamard inequality (H-H inequality) is a development of the concept of convexity, and it logically follows from Jensen’s inequality
The H-H inequality for convex functions has sparked a lot of attention, and several refinements and extensions have been investigated; see [3,4,5,6,7,8,9,10,11,12,13,14] and the references therein
Interval analysis is a subset of set-valued analysis and is concerned with the study of intervals in the context of mathematical analysis and topology
Summary
The Hermite–Hadamard inequality (see [1,2], p. 137) is a well-known inequality in convex function theory, with a geometrical explanation and a wide range of applications. Following the release of his book, a lot of scientists began to study interval arithmetic’s theory and applications. Khan et al presented the new class of convex fuzzy mappings known as (χ1 , χ2 )-convex fuzzy-interval-valued functions ((χ1 , χ2 )-convex F-I-V ·F) and obtained the new version of H-H inequalities for (χ1 , χ2 )-convex F-I-V ·Fs. Khan et al introduced new notions of generalized convex F-I-V ·Fs, and derived new fractional H-H type and H-H type inequalities for convex F-I-V ·Fs [27,28,29,30,31,32]. This study is organized as follows: Section 2 presents preliminary and new concepts and results in interval space, and convex analysis.
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