Generalized Trapezium-Type Inequalities via Modified (h,m)-Convex Functions of the Second Type

Abstract

In this article, we establish a generalized framework for integral inequalities by introducing an integral family of trapezoidal fractional estimates. Using a generalized weight function ϖ′(τ), we prove a new integral identity that establishes clear relationships between general fractional operators and differentiable functions. Using this result together with the classical Hölder, Power Mean, and Young inequalities, we derive several precise upper bounds for the trapezoidal remainder by assuming that the absolute value of the first derivative belongs to the class of modified convex (h,m)-functions of the second type. Throughout the work, we show that several seminal results reported in the literature are special cases of our own. Finally, we provide concrete applications to precise error estimates for special means.