Abstract
In this paper, we introduce some new paranormed sequence spaces and study some topological properties. Further, we determine α, β and γ-duals of the new sequence spaces and finally, we establish the necessary and sufficient conditions for characterization of matrix mappings.
Highlights
The idea to construct a new sequence space by means of the matrix domain of a particular limitation method has recently been employed by Altay and Basar[3, 4], Malkowsky and Savas[17], Basar et al.[7], Kirisci and Basar[11], Ng and Lee[18], Sonmez[21] and many more
Throughout the paper we denote w, ∞, c, c0 and p be the space of all, bounded, convergent, null and p-absolutely summable sequences respectively
We say that B defines a matrix mapping from X into Y, denoted by B : X → Y, if for every sequence x = ∈ X, the sequence Bx = (Bx)n is in Y where, (2.1)
Summary
The idea to construct a new sequence space by means of the matrix domain of a particular limitation method has recently been employed by Altay and Basar[3, 4], Malkowsky and Savas[17], Basar et al.[7], Kirisci and Basar[11], Ng and Lee[18], Sonmez[21] and many more. Altay and Basar [1, 2], Malkowsky[16] and Aydin and Basar[6] have employed on to construct new paranormed sequence spaces by means of the domain of some infinite matrices. The domain of generalized difference matrix B(r, s) on some Maddox’s spaces was studied by Aydin and Altay [5]. Domain of the double sequential band matrix B(r, s) on some Maddox’s spaces was studied by Ozger and Basar[19]
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