Double almost lacunary statistical convergence of order α

Ekrem Savaş

doi:10.1186/1687-1847-2013-254

Abstract

In this paper, we define and study lacunary double almost statistical convergence of order α. Further, some inclusion relations have been examined. We also introduce a new sequence space by combining lacunary double almost statistical convergence and Orlicz function.MSC:40B05, 40C05.

Highlights

1 Introduction The notion of convergence of a real sequence was extended to a statistical convergence by Fast [ ] as follows
If d(K) = d(K), we say that the natural density of K exists, and it is denoted by d(K
The double statistical convergence of order α is defined as follows

Summary

Introduction

The notion of convergence of a real sequence was extended to a statistical convergence by Fast [ ] (see Schoenberg [ ]) as follows. A sequence x = (xk) of real numbers is said to be statistically convergent to L if for arbitrary > , the set K( ) = {k ∈ N : |xk – L| ≥ } has a natural density zero. By [c ], we denote the space of strongly almost convergent double sequences. The double statistical convergence of order α is defined as follows.

Results

Conclusion