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

Abstract

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

Norm of matrix operator on Orlicz-binomial spaces and related operator ideal

“…An Orlicz function ϕ is a function from (0, ∞) to (0, ∞) which is continuous, increasing and convex with ϕ(0+) = 0 and so has a unique inverse ϕ −1 : (0, ∞) → (0, ∞). As usual in the Orlicz theory the domain of ϕ is extended to the real line by ϕ(x) = ϕ(|x|) and ϕ(0) = 0 (for details on Orlicz functions see [12,13,27]). Let x = (x n ) be a sequence of real numbers with x n > 0 for all n ∈ N 0 .…”