New type of Lacunary Orlicz Difference Sequence Spaces Generated By Infinite Matrices

Abstract

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