Table of Contents Author Guidelines Submit a Manuscript
International Journal of Analysis
Volume 2014, Article ID 945902, 8 pages
http://dx.doi.org/10.1155/2014/945902
Research Article

-Asymptotically Lacunary Equivalent Sequences

Department of Mathematics, Faculty of Education, Yüzüncü Yıl University, 65080 Van, Turkey

Received 2 July 2014; Accepted 22 September 2014; Published 3 December 2014

Academic Editor: Shamsul Qamar

Copyright © 2014 Tunay Bilgin. 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 introduce the strong -asymptotically equivalent and strong -asymptotically lacunary equivalent sequences which are some combinations of the definitions for asymptotically equivalent, statistical limit, modulus function, -convergence, and lacunary sequences. Then we use these definitions to prove strong -asymptotically equivalent and strong -asymptotically lacunary equivalent analogues of Connor’s results in Connor, 1988, Fridy and Orhan’s results in Fridy and Orhan, 1993, and Das and Patel’s results in Das and Patel, 1989.