Lacunary arithmetic statistical convergence

Taja Yaying; Bipan Hazarika

paper

Lacunary arithmetic statistical convergence

arXiv:1703.03780

Abstract

A lacunary sequence is an increasing integer sequence $θ = (k_{r})$ such that $k_{r} - k_{r - 1} \to \infty$ as $r \to \infty.$ In this article we introduce arithmetic statistically convergent sequence space $A S C$ and lacunary arithmetic statistically convergent sequence space $A S C_{θ}$ and study some inclusion properties between the two spaces. Finally we introduce lacunary arithmetic statistical continuity and establish some interesting results.

10 pages