Measures of Noncompactness in $\left(\bar{N}_{\Delta^{-}}^{q}\right)$ Summable Difference Sequence Spaces

Authors

  • Ishfaq Ahmad Malik Department of Mathematics National Institute of Technology, Srinagar
  • Tanweer Jalal National Institute of Technology, Srinagar

DOI:

https://doi.org/10.30495/jme.v13i0.936

Keywords:

Difference sequence space, BK spaces, matrix transformations, Measures of noncompactness

Abstract

In this paper we first introduce $\bar{N}_{\Delta^{-}}^{q}$ summable difference sequence spaces and prove some properties of these spaces. We then obtain the necessary and sufficient conditions for infinite matrices $A$ to map these sequence spaces on the spaces $c_0, c$ and $\ell_\infty$, the Hausdorff measure of noncompactness is then used to obtain the necessary and sufficient conditions for the compactness of the linear operators defined on these spaces.

Author Biographies

Ishfaq Ahmad Malik, Department of Mathematics National Institute of Technology, Srinagar

Research Scholar in

Department of Mathematics

National Institute of Technology, Srinagar

Tanweer Jalal, National Institute of Technology, Srinagar

Associate Professor

Department of Mathematics

National Institute of Technology, Srinagar

 

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Published

2019-04-10

Issue

Vol. 13

Section

Vol. 13, No. 4, (2019)

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