Open AccessOn composition operators of Fibonacci matrix and applications of Hausdorff measure of noncompactness
Author(s) -
Bipan Hazarika,
Anupam Das,
Emrah Evren Kara,
Feyzı Başar
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.39960
Subject(s) - hausdorff space , lambda , mathematics , combinatorics , banach space , measure (data warehouse) , space (punctuation) , matrix (chemical analysis) , dual polyhedron , fibonacci number , type (biology) , hausdorff measure , discrete mathematics , hausdorff dimension , physics , materials science , ecology , linguistics , philosophy , database , computer science , optics , composite material , biology
The aim of the paper is introduced the composition of the two infinite matrices $\Lambda=(\lambda_{nk})$ and $\widehat{F}=\left( f_{nk} \right).$ Further, we determine the $\alpha$-, $\beta$-, $\gamma$-duals of new spaces and also construct the basis for the space $\ell_{p}^{\lambda}(\widehat{F}).$ Additionally, we characterize some matrix classes on the spaces $\ell_{\infty}^{\lambda}(\widehat{F})$ and $\ell_{p}^{\lambda}(\widehat{F}).$ We also investigate some geometric properties concerning Banach-Saks type $p.$Finally we characterize the subclasses $\mathcal{K}(X:Y)$ of compact operators by applying the Hausdorff measure of noncompactness, where $X\in\{\ell_{\infty}^{\lambda}(\widehat{F}),\ell_{p}^{\lambda}(\widehat{F})\}$ and $Y\in\{c_{0},c, \ell_{\infty}, \ell_{1}, bv\},$ and $1\leq p<\infty.$