On n-normed linear space valued strongly ∇r-Cesaro and strongly ∇r-lacunary summable sequences

In this article we introduce the spaces |σ1|(X, ∇r) and Nθ(X, ∇r) of Xvalued strongly ∇r-Cesaro summable and strongly ∇r-lacunary summable sequences respectively, where X, a real linear n-normed space and ∇r is a new difference operator, where r is a non-negative integer. This article extends the notion of strongly Cesaro summable and strongly lacunary summable sequences to n-normed linear space valued (n-nls valued) difference sequences. We study these spaces for existence of norm as well as for completeness. Further weinvestigate the relationship between these spaces.