-Statistically Convergent Function Sequences

Authors: O. Duman¹; C. Orhan²

Source: Czechoslovak Mathematical Journal, Volume 54, Number 2, June 2004 , pp. 413-422(10)

Publisher: Springer

Price: $47.00 plus tax (Refund Policy)

Abstract:

In the present paper we are concerned with convergence in

-density and

-statistical convergence of sequences of functions defined on a subset D of real numbers, where

is a finitely additive measure. Particularly, we introduce the concepts of

-statistical uniform convergence and

-statistical pointwise convergence, and observe that

-statistical uniform convergence inherits the basic properties of uniform convergence.

Keywords: pointwise and uniform convergence; -statistical convergence; convergence in -density; finitely additive measure; additive property for null sets

Document Type: Research article

DOI: http://dx.doi.org/10.1023/B:CMAJ.0000042380.31622.39

Affiliations: 1: Ankara University, Faculty of Science, Dept. of Mathematics, Tando gbreve an 06100, Ankara, Turkey, Email: oduman@science.ankara.edu.tr an 06100, Ankara, Turkey, Email: oduman@science.ankara.edu.tr "> 2: Ankara University, Faculty of Science, Dept. of Mathematics, Tando gbreve an 06100, Ankara, Turkey, Email: orhan@science.ankara.edu.tran 06100, Ankara, Turkey, Email: orhan@science.ankara.edu.tr">