On lacunary weak statistical convergence of order α

Abstract

In this paper, we introduce lacunary weak statistical convergence of order α and weak $N_{\theta }^{\alpha }$-convergence for $0<\alpha \le 1$. We prove some properties of these modes of convergence and give some inclusion relations.

Keywords:

• Statistical convergence
• weak convergence
• lacunary sequence

2010 Mathematics Subject Classification:

• 40A35
• 40C05
• 40A05

Acknowledgments

The authors would like to thank the editor and the reviewers for their valuable comments and suggestions which resulted in substantial improvement in the presentation of the paper.