Almost Convergent Sequence Space Derived by Generalized Fibonacci Matrix and Fibonacci Core
Murat Candan *
Faculty of Arts Sciences, Department of Mathematics, Ä°nönü University, Malatya-44280, Turkey.
Kuddusi Kayaduman
Faculty of Arts Sciences, Department of Mathematics, Gaziantep University, Gaziantep-27310, Turkey.
*Author to whom correspondence should be addressed.
Abstract
Considerable interest in this article is to introduce the sequence space 
derived by generalized
difference Fibonacci matrix in which r,s ∈ 
\ {0}, also to discuss and compare with some wellknown
spaces defined previously. In addition to those, after demonstrating that the spaces 
and bc are linearly isomorphic, we have determined the β— and γ—duals of space 
and have
characterized some matrix classes on this space. As a conclusion, we have also found out that the
space has not a Schauder basis. Lastly, we have presented the Fibonacci core of a complex-valued
sequence and deal with inclusion theorems with respect to Fibonacci core type.
Keywords: Sequence spaces, almost convergence, Fibonacci matrix, -dual, matrix transformations, core theorems.