On double sequences of continuous functions having continuous p-limits ıı
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Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Univ Nis
Access Rights
info:eu-repo/semantics/openAccess
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 s(1,1)(x), s(1,2)(x) s(1,3)(x) ... s(2,1)(x), s(2,2)(x) s(2,3)(x) ... s(3,1)(x), s(3,2)(x) s(3,3)(x) ... have the following properties: 1. for each (m, n) s(m,n)(x) is continuous in A; 2. for each x in A we have P - lim(m,n) s(m,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 vertical bar s(m,n)(x)vertical bar <= M. Then there exists a T - transformation such that P - lim(m,n) sigma(m,n)(x) = s(x) uniformly in A and to that end we obtain the following. In order that the transformation be such that P - lim(s -> s0(S);t -> t0(T)) sigma(s;t;x) = 0 uniformly with respect x for every double sequence of continuous functions (s(m,n)(x)) define over A such that s(m,n)(x) is bounded over A and for all (m, n) and P - lim(m,n) s(m,n)(x) = 0 over A it is necessary and sufficient that P- lim(s -> s0(S);t -> t0(T)) Sigma(infinity,infinity)(k,l=1,1) vertical bar a(k,l)(s, t)vertical bar = 0
Description
Keywords
RH-Regular, Double Sequences, Pringsheim Limit Point, P-Convergent
Journal or Series
filomat
WoS Q Value
Q2
Scopus Q Value
Q2
Volume
27
Issue
5
