[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2015.55.4.909

Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

MANNA, ATANU (Department of Mathematics, Indian Institute of Technology Kharagpur)
MAJI, AMIT (Department of Mathematics, Indian Institute of Technology Kharagpur)
SRIVASTAVA, PARMESHWARY DAYAL (Department of Mathematics, Indian Institute of Technology Kharagpur)

Publication Information

Kyungpook Mathematical Journal / v.55, no.4, 2015 , pp. 909-931 More about this Journal

Abstract

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. 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.

Keywords

Sequence spaces; Difference operator; Generalized means; ${\alpha}$ -, ${\beta}$ -, ${\gamma}$ -duals; Matrix transformations; Rotundity; Kadec-Klee property;

Citations & Related Records

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