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On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core

DEMIRIZ, SERKAN;KARA, EMRAH EVREN;BASARIR, METIN

  • Received : 2013.12.22
  • Accepted : 2014.05.01
  • Published : 2015.06.23

Abstract

In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space $\hat{c}^f$. Also, we show that the spaces $\hat{c}^f$and $\hat{c}$ are linearly isomorphic. Further, we determine the ${\beta}$-dual of the space $\hat{c}^f$ and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.

Keywords

Sequence spaces;almost convergence;Fibonacci matrix;${\beta}$-dual;matrix transformations;core theorems

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