THE PARAMETERIZED INTEGRAL INEQUALITIES INVOLVING TWICE-DIFFERENTIABLE GENERALIZED n-POLYNOMIAL CONVEXITY UNDER THE FRAMEWORK OF FRACTAL DOMAINS AND ITS APPLICATIONS

The fractal [Formula: see text]-preinvex mappings are put forward and their properties are investigated firstly. Meanwhile, some fractal Hermite–Hadamard-type ([Formula: see text]) and Fejér–Hermite–Hadamard-type ([Formula: see text]) inequalities concerning [Formula: see text]-preinvexity are popularized. Then, two weighted parameterized [Formula: see text]-fractal identities are proposed, which involve twice the local fractional differentiable mappings. Based upon these identities and taking advantage of the fractal [Formula: see text]-preinvex mappings as well as [Formula: see text]-Lipschitzian mappings, a range of error estimations are deduced in the fractal domains. Finally, certain fractal inequalities with relation to the weighted formula and random variable are correspondingly presented as applications.

PROPERTIES AND 2α̃-FRACTAL WEIGHTED PARAMETRIC INEQUALITIES FOR THE FRACTAL (m,h)-PREINVEX MAPPINGS

ZHANG,

ZHOU,

2023

HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL

CHENG,

ZHAO,

SARIKAYA

2024

Fractional [Formula: see text]-calculus is considered to be the fractional analogs of [Formula: see text]-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) [Formula: see text]-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving [Formula: see text]-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF [Formula: see text]-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.

Some New Parametrized Inequalities on Fractal Set

XU,

LAKHDARI,

SALEH

et al. 2024

The aim of this study is to examine certain open three-point Newton–Cotes-type inequalities for differentiable generalized [Formula: see text]-convex functions on a fractal set. To begin, we introduce a novel parametrized identity involving the relevant formula, which yields various new findings as well as previously established ones. Finally, an example is given to demonstrate the accuracy of the new results and their graphical depiction. Moreover, we emphasize the applications of the results obtained.