Note on selection principles of Kocinac

Abstract

This paper investigates α d i , i ∈ {2, 3, 4}, selection principles (which are modification of known selection principles of Kočinac) on a double sequence of double sequences of real numbers which converge to a point a ∈ R in Pringsheim's sense. A stronger result than one given in [6] will be proved for the α d 2 selection principle. Also, two more propositions will be proved for the S d 1 and S φ 1 selection principles, which are also improvements of results given in [6]. Let a double sequence of real numbers x = (x m,n) m,n∈N and a point a ∈ R be given. Then:

Summation of double sequences and selection principles

“…Denote the class of such double sequences by c 0 2 and the class of such positive double sequences by c 0 2,+ (see [2]). Theory of double sequences (in particular, theory of convergence of double sequences in Pringsheim's sense) is important current part of mathematical analysis and other mathematical disciplines (see, e.g.…”

Exponent of convergence for double sequences and selection principles

“…Denote the class of such double sequences by c a 2 and the class of such positive double sequences by c a 2,+ (see [6]). A variation of (1) is given in [5].…”