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Statistical quasi Cauchyness in two normed spaces

Functional Analysis 2014-02-17 v1

Abstract

A function ff defined on a subset EE of a two normed space XX is statistically ward continuous if it preserves statistically quasi-Cauchy sequences of points in EE where a sequence (xn)(x_n) is statistically quasi-Cauchy if (Δxn)(\Delta x_{n}) is a statistically null sequence. A subset EE of XX is statistically ward compact if any sequence of points in EE has a statistically quasi-Cauchy subsequence. In this paper, new kinds of continuities are investigated in two normed spaces. It turns out that uniform limit of statistically ward continuous functions is again statistically ward continuous.

Keywords

Cite

@article{arxiv.1402.3291,
  title  = {Statistical quasi Cauchyness in two normed spaces},
  author = {Huseyin Cakalli and Sibel Ersan},
  journal= {arXiv preprint arXiv:1402.3291},
  year   = {2014}
}

Comments

11 pages

R2 v1 2026-06-22T03:07:59.649Z