10.1007/s40096-021-00396-3

Compact operators on spaces of binomial fractional difference sequences

  • Anu Choudhary1,
  • Kuldip Raj1,
  • M. Mursaleen*2,
  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, 182320, IN
  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, IN Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, TW

Published in Issue 2021-04-12

How to Cite

Choudhary, A., Raj, K., & Mursaleen, M. (2021). Compact operators on spaces of binomial fractional difference sequences. Mathematical Sciences, 16(1 (March 2022). https://doi.org/10.1007/s40096-021-00396-3
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Abstract

Abstract In this paper, we intend to form certain estimates and identities for the norm of matrix operator from ℓr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{r}$$\end{document} -type binomial fractional difference sequence space into c,c0,ℓ∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c, c_{0}, \ell _{\infty }$$\end{document} and ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{1}$$\end{document} sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on ℓr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{r}$$\end{document} -type binomial fractional difference sequence space (1≤r<∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(1 \le r < \infty )$$\end{document} by employing the Hausdorff measure of non-compactness.

Keywords

  • Fractional difference operator,
  • Binomial matrix,
  • Compact operator,
  • Operator norm,
  • Hausdorff measure of noncompactness

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