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Abstract and Applied Analysis
Volume 2017 (2017), Article ID 9828065, 6 pages
https://doi.org/10.1155/2017/9828065
Research Article

Approximation Properties of -Bernoulli Polynomials

Near East University, Lefkosa, Northern Cyprus, Mersin 10, Turkey

Correspondence should be addressed to M. Momenzadeh; moc.liamg@1hedaznemomm

Received 8 August 2017; Accepted 29 October 2017; Published 3 December 2017

Academic Editor: Allan Peterson

Copyright © 2017 M. Momenzadeh and I. Y. Kakangi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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