A Robust Approach About Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

Abstract

In this new study, which deals with the different properties of $\ell_{p}(\widehat{F}(r,s))$ $(1\leq p<\infty)$ and $\ell_{\infty}(\widehat{F}(r,s))$ spaces defined by Candan and Kara in 2015 by using Fibonacci numbers according to a certain rule, we have tried to review all the qualities and features that the authors of the previous editions have found most useful. This document provides everything needed to characterize the matrix class $(\ell_{1},\ell_{p}(\widehat{F}% (r,s)))$ $(1\leq p<\infty)$. Using the Hausdorff measure of noncompactness, we simultaneously provide estimates for the norms of the bounded linear operators $L_{A}$ defined by these matrix transformations and identify requirements to derive the corresponding subclasses of compact matrix operators. The results of the current research can be regarded as to be more inclusive and broader when compared to the similar results available in the literature.

Keywords

• Sequence spaces
• Fibonacci numbers
• Compact operators
• Hausdorff measure of noncompactness

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