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Certain sequence spaces and related duals with respect to the $b$-metric

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The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the $b$-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of $b$-bounded, $b$-convergent and $b$-null sequences.

Abstract

The aim of this paper is to present the classical sets of sequences and related matrix transformations with respect to the $b$-metric. Also, we introduce the relationships between these sets and their classical forms with corresponding properties including convergence and completeness. Further we determine the duals of the new spaces and characterize matrix transformations on them into the sets of $b$-bounded, $b$-convergent and $b$-null sequences.

참고문헌 (25)

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