Patterson, Richard F.Savaş, Ekrem2015-09-092015-09-0920131029-242Xhttps://hdl.handle.net/11467/1141http://dx.doi.org/10.2298/FIL1305931PThe 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 = 0eninfo:eu-repo/semantics/openAccessRH-RegularDouble SequencesPringsheim Limit PointP-ConvergentArticle275931935Q2WOS:000322038400022Q22-s2.0-84880175260