Hermite-Hadamard type inequalities involving $s$-convex function in the first sense

In this paper we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values of the first derivatives are $s$-convex in the first sense. By means of the obtained inequalities, some bound functions involving beta functions and digamma function are derived as applications. Furthermore, they are used to obtain an error bound in numerical integration of certain $s$-convex functions by composite trapezoid rule.