Matrix mappings and Hausdorff measure of non-compactness on Riesz difference spaces of fractional order - Yaying, Taja; Hazarika, Bipan; Et, Mikail (Springernature, 2021)
In this paper we introduce sequence spaces r0t(Delta Bq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>t_0(\varDelta <^>{Bq})$$\end{document} and rct(Delta Bq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>t_c(\varDelta <^>{Bq})$$\end{document} defined by the domain of generalized Riesz difference matrix Rt Delta Bq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R<^>t\varDelta <^>{Bq}$$\end{document} of fractional order q in the sequence spaces c0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_0$$\end{document} and c, respectively. We obtain alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-, beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}- and gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document}-duals and investigate certain results related to matrix transformations on the spaces r0t(Delta Bq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>t_0(\varDelta <^>{Bq})$$\end{document} and rct(Delta Bq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>t_c(\varDelta <^>{Bq})$$\end{document}. Finally, using Hausdorff measure of noncompactness, we characterize certain classes of compact operators on r0t(Delta Bq)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r<^>t_0(\varDelta <^>{Bq})$$\end{document} space.
Keywords: Riesz difference sequence space; Difference operator DeltaBq; documentclass[12pt]{minimal}; usepackage{amsmath}; usepackage{wasysym}; usepackage{amsfonts}; usepackage{amssymb}; usepackage{amsbsy}; usepackage{mathrsfs}; usepackage{upgreek}; setlength{; oddsidemargin}{-69pt}; begin{document}$$; varDelta <^>{Bq}$$; end{document}; Matrix Transformation; Compact operator; Hausdorff measure of non-compactness