• Title/Summary/Keyword: Rotundity

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Some Paranormed Difference Sequence Spaces Derived by Using Generalized Means

  • MANNA, ATANU;MAJI, AMIT;SRIVASTAVA, PARMESHWARY DAYAL
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.909-931
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    • 2015
  • 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.