Some New Improvements of Hermite-Hadamard Type Inequalities Using Strongly $(s,m)$-Convex Function with Applications

The trapezoidal-type inequalities are discovered in this study using the fractional operator, which produces powerful results. We established a general identity for Caputo-Fabrizio integral operators and the second derivative function. Using this identity new error bounds and estimates for strongly $(s,m)$-convex functions are obtained. Moreover, some noveltrapezoidal-type inequalities are offered taking this identity into account using the known inequalities like Young, Jensen, H"{o}lder and power-mean inequalities. Finally, we present some applications for matrix inequality, estimation error regarding trapezoidal formulas and special means for real numbers.