Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means
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This paper presents some new paranormed sequence spaces X(r, s, t, p ; Δ) where X∈{ l∞(p), c(p), c0(p), l(p)} defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the α-, β-, γ- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from X(r, s, t, p ; Δ) to X. Finally, it is proved that the sequence space l(r, s, t, p ; Δ) is rotund when pn>1 for all n and has the Kadec-Klee property.
Abstract
This paper presents some new paranormed sequence spaces X(r, s, t, p ; Δ) where X∈{ l∞(p), c(p), c0(p), l(p)} defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the α-, β-, γ- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from X(r, s, t, p ; Δ) to X. Finally, it is proved that the sequence space l(r, s, t, p ; Δ) is rotund when pn>1 for all n and has the Kadec-Klee property.
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