Lacunary Statistical Convergence of Multiple Sequences

Abstract

Quite recently, Mursaleen and Edely [M. Mursaleen, O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. (in press)], defined the statistical analogue for double sequences x = {(xk,1)} as follows: A real double sequence x = {x(k,l)} is said to be P-statistically convergent to L provided that for each epsilon > 0 P - lim(m,n) 1/mn {numbers of (j, k) : j < m and k < n, vertical bar x(j,k) - L vertical bar >=epsilon}. In this paper we introduce and study lacunary statistical convergence for double sequences and we shall also present some inclusion theorems. (c) 2005 Published by Elsevier Ltd.