Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers

Yıl 2014, Cilt: 14 Sayı: 1, 1 - 3, 01.04.2014

Shyamal Debnath Subrata Saha

Öz

The main purpose of this paper is to introduce the new sequence spaces (F), c(F) and (F) based on the newly defined regular matrix F of Fibonacci numbers. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. Let w be the space of all real sequences. Any vector subspace of w is called a sequence space. We shall write c, and for the sequence spaces of all convergent, null and bounded sequences. Let X, Y be two sequence spaces and A = ( ) be an infinite matrix of real numbers , where n, k N.Then, A defines a matrix mapping ( Debnath and Debnath, communicated; Malkowsky and Rakocevic, 2007) from X into Y and we denote it by A : X  Y, if for every sequence x= ( )  X, the sequence Ax = { (x)+ , the A-transform of x, is in Y; where (x) = ∑ , (n N)

Anahtar Kelimeler

Newly, Defined, Sequence

Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers

Öz

The main purpose of this paper is to introduce the new sequence spaces (F), c(F) and (F) based on the newly defined regular matrix F of Fibonacci numbers. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. Let w be the space of all real sequences. Any vector subspace of w is called a sequence space. We shall write c, and for the sequence spaces of all convergent, null and bounded sequences. Let X, Y be two sequence spaces and A = ( ) be an infinite matrix of real numbers , where n, k N.Then, A defines a matrix mapping ( Debnath and Debnath, communicated; Malkowsky and Rakocevic, 2007) from X into Y and we denote it by A : X  Y, if for every sequence x= ( )  X, the sequence Ax = { (x)+ , the A-transform of x, is in Y; where (x) = ∑  , (n N)

Anahtar Kelimeler

Fibonacci Number, Regular Matrix, Sequence Space

Kaynakça

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