Real, complex and functional analysis

New generalized weighted fractional variants of Hermite–Hadamard inequalities with applications

J. E. Nápoles^ab, B. Bayraktar^c, S. I. Butt<sup>d

a</sup> UNNE FaCENA, Ave. Libertad 5450, Corrientes 3400, Argentina
^b UTN-FRRE, French 414 Resistencia, Chaco 3500, Argentina
^c Bursa Uludag University Faculty of Education, Gorukle Campus, Bursa, Turkey
^d COMSATS University, Lahore Campus, Islamabad, Pakistan

Abstract: Integral inequalities play a fundamental role in various mathematical fields, which have led to new methods and theoretical developments, both pure and applied. The need for searching for precise inequalities, in which the notion of convexity plays an important role, has a high impact on approximation theory calculus. In this paper, we first obtained a new version of the weighted fractional identity that led us to obtain new variants of weighted Hermite–Hadamard and Bullen type inequalities. We then presented several refinements of it in the framework of weighted integrals for the modified second type $(h,m)$–convex functions.

Keywords: Hermite–Hadamard integral inequality, Bullen type inequality, Hölder's inequality, $(h,m)-$convex modified functions, weighted fractional integrals operators.

UDC: 517.218.244,517.518.86

MSC: 26D10, 26A51, 26A33

Received February 11, 2023, published September 30, 2024

Language: English

DOI: 10.33048/semi.2024.21.047