On Error Bounds for Parameterized Trapezoid and Newton Formulas via Conformable Fractional Operators

Year 2026, Volume: 18 Issue: 1, 192 - 208, 23.02.2026

Fatih Hezenci , Erhan Set , Hüseyin Budak

https://doi.org/10.47000/tjmcs.1571950

https://izlik.org/JA75WU53PW

Abstract

In this paper, we are established that the parameterized inequalities reduce to some trapezoid and
Newton-type inequalities with the help of the special choices. For this, first we present a parameterized integral identity inducing fractional integrals and then prove trapezoid and Newton-type inequalities for differentiable convex functions. These inequalities are proved by using the conformable fractional integrals. By using the special cases of our main results, we also give some new and previously obtained trapezoid and Newton-type inequalities.

Keywords

Trapezoid inequality , Simpson's $\frac{3}{8}$ formula , conformable integrals , convex functions

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