On Generalized Maddox Spaces via Difference Operator
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Authors: S. MAHARANA AND P. BALIARSINGH
DOI: 10.46793/KgJMat2608.1221M
Abstract:
In the present work, we begin our investigation with some dynamic properties of new generalized difference operator Δhα,β,γ, defined in Baliarsingh [?]. Combining this operator with the well known Cesàro operator, we also introduce new classes of generalized Cesàro summable difference sequence spaces w(Δhα,β,γ,p),w0(Δhα,β,γ,p) and w∞(Δhα,β,γ,p), which are the natural extension of the spaces wp, w0p and w∞p defined in [?] and w0(p), w(p), and w∞(p) defined by Maddox [?]. We establish various topological properties on these spaces along with some inclusion relations with other basic sequence spaces. Further, our investigation is carried out to determine α∗- and β∗- duals and characterize matrix transformations on these spaces.
Keywords:
Sequence spaces, difference operators, topological properties, matrix transformations, dual spaces.
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