Title

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

Document Type

Article

Publication Date

7-19-2013

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.

Publication Title

Filomat

Volume

27

Issue

5

First Page

931

Last Page

935

Digital Object Identifier (DOI)

10.2298/FIL1305931P

ISSN

03545180

Share

COinS