On double sequences of continuous functions having continuous P-limits II
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.
Digital Object Identifier (DOI)
Patterson, & Savaș, E. (2013). On double sequences of continuous functions having continuous P-limits II. Filomat, 27(5), 931–935. https://doi.org/10.2298/FIL1305931P