Annals of Communications in Mathematics

AbstractThe concept of statistical summability C, 1)(H, 1) has recently been introduced by [8]. In this paper we establish some inequalities related to concept of statistical summability (C, 1)(H, 1).

ABSTRACT.This paper introduces statistical gauge convergence as a refinement of statistical convergence in metric spaces, where deviations from the limit are controlled by positive continuous functions rather than fixed constants. We provide equivalent density based characterizations and examine their relationship with both classical and statistical convergence, showing that the corresponding implications are strict in general. Further more, we investigate the topology generated by this convergence and prove that it is typically finer than the underlying metric topology. Several examples are included to clarify the hierarchical structure among the considered notions of convergence.