Hüseyin Budak

S.Erden and H.Budak, “Fractional Integral Inequalities of Riemann–Liouville Type for Higher-Order Differentiable Convex Mappings,” Mathematical Methods in the Applied Sciences (2026): 1–11, https://doi.org/10.1002/mma.70690. 1 Introduction The Hermite-Hadamard inequality, a fundamental result in convex analysis, provides a useful characterization for convex functions.

1 Introduction The finding of upper bounds of errors using numerical integration formulas and different techniques has been researched by many mathematicians. Many papers are devoted to the mathematical inequalities with various function classes such as convex, bounded, and Lipschitzian functions to find the error bounds of numerical integration formulas. The Newton quadratic formula is given as follows: ∫ σ 1 σ 2 F ϵ d ϵ ≈ σ 2 − σ 1 8 F σ 1 + 3 F 2 σ 1 + σ 2 3 + 3 F σ 1 + 2 σ 2 3 + F σ 2 .

Quantum calculus extends classical calculus through the inclusion of a parameter , thereby broadening the conceptual framework for analysis. The present study provides novel variants of Boole's formula-type inequalities for -differentiable convex functions via first deriving an essential quantum-integral identity. The derived results enhance classical findings and highlight the distinctive properties of convex functions in quantum calculus.