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arXiv · 1307.5884

Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

Atanu Manna·Amit Maji·P. D. Srivastava
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Abstract

This paper presents new sequence spaces $X(r, s, t, p ;\Delta)$ for $X \in \{l_\infty(p), c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete under a suitable paranorm. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;\Delta)$ to $X$. Finally, it is proved that the sequence space $l(r, s, t, p ;\Delta)$ is rotund when $p_n>1$ for all $n$ and has the Kadec-Klee property.

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Atanu Manna, Amit Maji, P. D. Srivastava. 2013-07-19. Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means. https://doi.org/10.5666/kmj.2015.55.4.909

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