Interval Fejér-Type Inequalities for Left and Right-λ-Preinvex Functions in Interval-Valued Settings

Abstract

For left and right λ-preinvex interval-valued functions (left and right λ-preinvex IVFs) in interval-valued Riemann operator settings, we create Hermite–Hadamard (H-H) type inequalities in the current study. Additionally, we create Hermite–Hadamard–Fejér (H-H-Fejér)-type inequalities for preinvex functions of the left and right interval-valued type under some mild conditions. Moreover, some exceptional new and classical cases are also obtained. Some useful examples are also presented to prove the validity of the results.

Generalized Preinvex Interval-Valued Functions and Related Hermite–Hadamard Type Inequalities

“…A sequence of operators need not h an identity limit, according to a Korovkin-type theorem found by Guessab et al [18]. ditionally, Guessab [19] worked on ideas such as bivariate Hermite interpolation From ( 25) and ( 26), we have where 𝔖: 𝕀 ⊂ ℝ → ℝ, is a convex function on closed bound interval 𝕀 of ℝ, and 𝜍, 𝜐 ∈ 𝕀 with 𝜍 < 𝜐, and for applications of the Hermite-Hadamard integral inequality, see [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”

“…It is frequently used in the literature and outlines the prerequisites and extenuating circumstances for a function to be convex. Using Riemann-Liouville fractional integrals, Sarikaya et al [14] where 𝔖: 𝕀 ⊂ ℝ → ℝ, is a convex function on closed bound interval 𝕀 of ℝ, and 𝜍, 𝜐 ∈ 𝕀 with 𝜍 < 𝜐, and for applications of the Hermite-Hadamard integral inequality, see [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”

“…(1) > 0, and Condition C for γ, then where 𝔖: 𝕀 ⊂ ℝ → ℝ, is a convex function on closed bound interval 𝕀 of ℝ, and 𝜍, 𝜐 ∈ 𝕀 with 𝜍 < 𝜐, and for applications of the Hermite-Hadamard integral inequality, see [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”

“…where S : I ⊂ R → R , is a convex function on closed bound interval I of R, and ς, υ ∈ I with ς < υ, and for applications of the Hermite-Hadamard integral inequality, see [3][4][5][6][7][8][9][10][11][12][13] and the references therein. Different integral inequalities have been discovered for different integrals operators.…”

“…Convex polytopes and Jensen type inequalities proposals were the subject of Guessab's [17] study, which also looked at approximation error in convex functions. A sequence of operators need not have where 𝔖: 𝕀 ⊂ ℝ → ℝ, is a convex function on closed bound interval 𝕀 of ℝ, and 𝜍, 𝜐 ∈ 𝕀 with 𝜍 < 𝜐, and for applications of the Hermite-Hadamard integral inequality, see [3][4][5][6][7][8][9][10][11][12][13] and the references therein.…”