Abstract:

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)

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