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

Year 2024, , 48 - 59, 31.01.2024

Murat Candan

https://doi.org/10.54974/fcmathsci.1303769

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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