Almost Convergent Sequence Space Derived by Generalized Fibonacci Matrix and Fibonacci Core

Considerable interest in this article is to introduce the sequence space rs1.JPGderived by generalized
difference Fibonacci matrix in which r,s ∈ \mathbb{R} \ {0}, also to discuss and compare with some wellknown
spaces defined previously. In addition to those, after demonstrating that the spaces rs2.JPG
and bc are linearly isomorphic, we have determined the β— and γ—duals of space rs3.JPG 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.