New type of Lacunary Orlicz difference sequence spaces generated by infinite matrices

Abstract

The main purpose of this paper is to introduce the spaces ?o? [A,M,?, p] and ?? [A,M,?,p] and ???[A,M,?,p] generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of ?? [A,?]-statistical convergence and derive some results between the spaces ?? [A,?] and ??[A,?]. Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space ???? [A,?,p]. Finally, we introduce the notion of ??[A,?]-statistical convergence of order ? of real number sequences and obtain some inclusion relations between the set of ?[A,?]-statistical convergence of order ?.