Original scientific paper

Lacunary statistical convergence of double sequences

R. F. Patterson
E. Savaş

Abstract

In 1978 Freedman, Sember, and Raphael presented a definition for
lacunary refinement as follows: $\rho=\{\bar{k}_{r}\}$ is called a
lacunary refinement of the lacunary sequence $\theta =\{k_{r}\}$
if $\{k_{r}\}\subseteq \{\bar{k}_{r}\}$. They use this definition
to present one side inclusion theorem with respect to the refined
and non refined sequence. In 2000 Li presented the other side of
the inclusion. In this paper we shall present a multidimensional
analogue to the notion of refinement of lacunary sequences and use
this definition to present both sides of the above inclusion
theorem. In addition, we shall also present a notion of double
lacunary statistically Cauchy and use this definition to establish
that it is equivalent to the $S_{\theta_{r,s}}$-P-convergence.

Keywords

double lacunary sequences; P-convergent

Hrčak ID:

660

URI

https://hrcak.srce.hr/660

Publication date:

23.6.2005.

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