Characterization of uniform statistical convergence for double sequences

Abstract

In the present study we introduce uniform statistical convergence for double sequences. We present a decomposition theorem that characterizes uniform statistical convergence for double sequences.

Some results on uniform statistical cluster points

“…One of the most important generalizations is uniform statistical convergence. This type of convergence has been introduced by Brown and Freedman [3] by using uniform density and has been studied by many authors in various directions [2,14,15,19,20]. This type of convergence is stronger than ordinary convergence and so it is quite effective, especially when the classical limit does not exist.…”

I-convergence of multiple sequences in cone metric spaces

“…As is well known, to extend the set of convergent sequences, Fast and Schoenberg independently introduced the concept of statistical convergence [13,14]. Since then, this concept was studied byŠalát [15], Fridy [16] and Connor [17] and many others [18,19,11,12].…”