Abstract. In this paper we will present a definition for lacunary $P$-convergent double sequences analogues to the definition presented by Freedman, Sember and Raphael in 1978. This definition shall be used to establish a connection between the strongly double Cesaro summable and strongly double lacunary convergent sequences, and the connection strongly double almost convergence and strongly double lacunary convergent sequence. Also, we investigate inclusion relations among these spaces.

AMS Subject Classification (1991): 40A05, 40G05

Keyword(s): Double sequence, Lacunary sequence, Almost convergence, Cesaro summable.

Received January 5, 2004, and in final form September 15, 2004. (Registered under 5862/2009.)