Some Generalized Fibonacci Difference Spaces Defined by a Sequence of Modulus Functions

Abstract

This paper submits the sequence space $l\left( \widehat{F}\left( r,s\right),\mathcal{F},p,u\right) $ and $l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) $of non-absolute type under the domain ofthe matrix$\widehat{\text{ }F}\left( r,s\right) $ constituted by usingFibonacci sequence and non-zero real number $r$, $s$ and a sequence ofmodulus functions. We study some inclusion relations, topological andgeometric properties of these spaceses. Further, we give the $\alpha $- $%\beta $- and $\gamma $-duals of said sequence spaces and characterization ofthe classes $\left( l\left( \widehat{F}\left( r,s\right) ,\mathcal{F}%,p,u\right) ,X\right) $ and $\left( l_{\infty }\left( \widehat{F}\left(r,s\right) ,\mathcal{F},p,u\right) ,X\right) $.

Compact Operators on the Sets of Fractional Difference Sequences

“…We refer to [4,11,12,[14][15][16][17][18][27][28][29][30][31][32][33] for further studies in theory of -spaces and its applications. In order to give full knowledge on the measure of noncompactness in the sequence spaces and the sets of fractional difference sequence spaces we refer to [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50].…”