On Some Error Bounds of Maclaurin's Formula for Convex Functions in q-Calculus

Abstract

The main goal of this paper is to establish some error bounds for Maclaurin's formula which is three point quadrature formula using the notions of q-calculus. For this, we first prove a $q$-integral identity involving fist time $q$-differentiable functions. Then, by using the newly established identity we find the error bounds for Maclaurin's formula by using the convexity of fist time $q$-differentiable functions. It is also shown that the newly established inequalities are extensions of some existing inequalities inside the literature.