Spaces of Cesaro difference sequences of order r defined by a modulus function in a locally convex space

Abstract

The idea of difference sequence spaces was introduced by Kizmaz [12] and was generalized by Et and Colak [6]. In this paper we introduce and examine some properties of the sequence spaces [V, lambda, f, p](0)(Delta(r)(v), q), [V, lambda, f, p],(Delta(r)(v), q), [V, lambda, f, p](infinity) (Delta(r)(v), q), S-lambda(Delta(r)(v), q) and give some inclusion relations on these spaces. We also show that the space S-lambda (Delta(r)(v), q) may be represented as a [V, lambda, f, p](1) (Delta(r)(v),q) space. Furthermore, we compute Kothe-Toeplitz duals of the spaces of generalized Cesaro difference sequences spaces.