On some n-normed linear space valued difference sequences

The main aim of this article is to extend the notion of strongly Cesàro summable and strongly lacunary summable real sequences to n-normed linear space valued (n-nls valued) difference sequences. Consequently we introduce the spaces |σ1|(X,∇) and Nθ(X,∇), respectively, where X is an n-normed space and ∇ is a difference operator. We investigate these spaces for completeness as well as for the relationship between these spaces.