Approximation properties of q-Bernoulli polynomials

Abstract

We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of truncated series of q-Bernoulli polynomials and the error is calculated. This paper can be helpful in two different branches, first solving differential equations by estimating functions and second we may apply these techniques for operator theory.