A New Highly Accurate Approach to Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

Abstract

The current research examines the many characteristics of the $\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ $(1\leq p<\infty)$ and $\ell_{\infty}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ spaces which are the generalized forms of those by Candan in 2024 using Fibonacci numbers and two non-zero real numbers in accordance with a predetermined rule, we have made an effort to go through all the characteristics and features which the author of earlier versions thought are the most valuable. This manuscript contains all the information required to describe the matrix class $(\ell_{1},\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s})))$ $(1\leq p<\infty)$ which are going to be given in detail in the following sections of the manuscript. We are going to offer estimates for the norms of the bounded linear operators $L_{A}$ formed by those matrix transformations utilizing the Hausdorff measure of non-compactness and identify prerequisites to derive the relevant subclasses of compact matrix operators. When the findings of the current study are compared to those found in the literature, it can be said that the newly found ones are more inclusive and comprehensive.