ON I-LACUNARY ARITHMETIC STATISTICAL CONVERGENCE

Abstract

In this paper, we introduce arithmetic I-statistically convergent sequence space AISC, I-lacunary arithmetic statistically convergent sequence space AISC(theta), strongly I-lacunary arithmetic convergent sequence space AN(theta) [I] and prove some inclusion relations between these spaces. Futhermore, we give I-lacunary arithmetic statistical continuity. Finally, we define I-Cesaro arithmetic summability, strongly I-Cesaro arithmetic summability. Also, we investigate the relationship between the concepts of strongly I-Cesaro arithmetic summability, strongly I-lacunary arithmetic summability and arithmetic I -statistically convergence.