Generalized Statistical Convergence for Sequences of Function in Random 2-Normed Spaces


Gürdal M., Savaş E.

in: Mathematics and Computing, Ghosh D.,Giri D.,Mohapatra R.,Savas E.,Sakurai K.,Singh L., Editor, Springer Nature, Basel, pp.296-308, 2018

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2018
  • Publisher: Springer Nature
  • City: Basel
  • Page Numbers: pp.296-308
  • Editors: Ghosh D.,Giri D.,Mohapatra R.,Savas E.,Sakurai K.,Singh L., Editor

Abstract

In this paper, we introduce a new type of convergence for a sequence of function, namely, {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistically convergent sequences of functions in random 2-normed space, which is a natural generalization of convergence in random 2-normed space. In particular, following the line of recent work of Karakaya et al. [12], we introduce the concepts of uniform {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistical convergence and pointwise {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistical convergence in the topology induced by random 2-normed spaces. We define the {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistical analog of the Cauchy convergence criterion for pointwise and uniform {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistical convergence in a random 2-normed space and give some basic properties of these concepts. In addition, the preservation of continuity by pointwise and uniform {\$}{\$}{\backslash}lambda {\$}{\$}$\lambda$-statistical convergence is proven