On deferred f-statistical convergence for double sequences

Abstract

In this article, we first put forward the concept of deferred f-double natural density for double sequences, where f is an unbounded modulus. Then, we combine f-density with deferred statistical convergence for double sequences and investigate deferred f-statistical convergence and strongly deferred Cesàro summability with respect to modulus f. Moreover, we extend these concepts to deferred f-statistical convergence for double sequences of random variables in the Wijsman sense and prove some inclusions. Finally, we consider the concepts of deferred f-statistical convergence of order α\alpha and strongly deferred f-summability of order α\alpha for double sequences and obtain some conclusions.

Keywords

• deferred f-statistical convergence
• double sequences
• strongly deferred cesàro summability
• in the wijsman sense
• 40a35
• 40g05
• 40g15