Abstract
The statistical convergence in metric spaces is considered. Its equivalence to the statistical fundamentality in complete metric spaces is proved. Introduced the concept of $p$-strong convergence, and proved its equivalence to the statistical convergence. Tauberian theorems concerning statistical convergence in metric spaces are given.
Highlights
The idea of statistical convergence was first proposed by A.Zigmund (Zygmund, 1979) in his famous monograph where he talked about ”almost convergence”
The study of statistical convergence in metric spaces is of special scientific interest
Statistical convergence is currently actively used in many areas of mathematics such as summation theory
Summary
The idea of statistical convergence was first proposed by A.Zigmund (Zygmund, 1979) in his famous monograph where he talked about ”almost convergence”. The study of statistical convergence in metric spaces is of special scientific interest. Fridy, 1985) who proved its equivalence to statistical convergence with respect to numerical sequences. This problem was raised in (G.D. Maio and L.D.R. Kocinac, 2008) concerning uniform space (X; U). In this paper we consider the statistical convergence in metric spaces. Concept p-strong convergence in metric spaces is introduced and prove its equivalence to the one of statistical convergence. It should be noted that the issue of statistical convergence in metric spaces considered in In these papers the statistical boundedness, the statistical equivalence of sequences in metric spaces and their relationship to the statistical convergence are considered
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