RUS  ENG
Full version
JOURNALS // Problemy Analiza — Issues of Analysis // Archive

Probl. Anal. Issues Anal., 2025 Volume 14, Issue 2, Pages 25–52 (Mi pa421)

Inequalities of the $3/8$-Simpson type for differentiable functions via generalized fractional operators

B. Bayraktara, L. Gómezb, J. E. Nápolesbc

a Bursa Uludag University, Faculty of Education, Gorukle Campus, 16059, Bursa, Turkey
b UNNE-FaCENA, Ave. Libertad 5450, Corrientes 3400, Argentina
c UTN-FRRE, French 414, Resistencia, Chaco 3500, Argentina

Abstract: Simpson-type inequalities are an important tool in mathematical analysis, particularly in the study of integrals. In this paper, we present new generalized $3/8$-Simpson-type inequalities for functions whose first derivative modulus is $(h, m)$-convex and satisfies the Lipschitz condition via weight integral operators. To obtain these results, we use a new integral identity established in our study. This research generalizes, extends, and complements the existing results in the literature.

Keywords: convex function, $(h, m)$-convex function, Simpson-type inequality, weighted integral operator, Hölder inequality, Power mean inequality, Young inequality, Lipschitz function.

UDC: 517.218.244, 517.518.862

MSC: 26A51, 6A33, 226D10

Received: 13.12.2024
Revised: 11.03.2025
Accepted: 22.03.2025

Language: English

DOI: 10.15393/j3.art.2025.17330



© Steklov Math. Inst. of RAS, 2025