On double sequences of continuous functions having continuous P-limits II

Pattersona R. F., Savaş E.

Filomat, vol.27, no.5, pp.931-935, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 5
  • Publication Date: 2013
  • Doi Number: 10.2298/fil1305931p
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.931-935
  • Keywords: Double sequences, P-convergent, Pringsheim limit point, RH-regular
  • Uşak University Affiliated: No

Abstract

The goal of this paper is to relax the conditions of the following theorem: Let A be a compact closed set; let the double sequence of function have the following properties: 1. for each (m, n) sm,n(x) is continuous in A; 2. for each x in A we have P - limm,n sm,n(x) = s(x); 3. s(x) is continuous in A; 4. there exists M such that for all (m, n) and all x in A |sm,n(x)| ≤ M. Then there exists a T-transformation such that and to that end we obtain the following. In order that the transformation be such that uniformly with respect x for every double sequence of continuous functions (sm,n(x)) define over A such that sm,n(x) is bounded over A and for all (m, n) and P-limm,n sm,n(x) = 0 over A it is necessary and sufficient that.