TY  - JOUR
T1  - Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers
TT  - Some Newly Defined Sequence Spaces Using Regular Matrix of Fibonacci Numbers
AU  - Debnath, Shyamal
AU  - Saha, Subrata
PY  - 2014
DA  - April
JF  - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi
PB  - Afyon Kocatepe University
WT  - DergiPark
SN  - 2149-3367
SP  - 1
EP  - 3
VL  - 14
IS  - 1
LA  - en
AB  - 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)
KW  - Fibonacci Number
KW  - Regular Matrix
KW  - Sequence Space
N2  - 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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UR  - https://dergipark.org.tr/en/pub/akufemubid/issue//19918
L1  - https://dergipark.org.tr/en/download/article-file/18507
ER  -