Generalized vector valued double sequence space using modulus function

Authors

  • Anindita Basu
  • P. D. Srivastava

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.69

Abstract

In this paper, we introduce a generalized vector valued paranormed double sequence space $ F^{2}(E,p,f,s) $, using modulus function $ f $, where $ p=(p_{nk}) $ is a sequence of non-negative real numbers, $ s\geq 0 $ and the elements are chosen from a seminormed space $ (E, q_{E}) $. Results regarding completeness, normality, $ K_{2} $-space, co-ordinatewise convergence etc. are derived. Further, a study of multiplier sets, ideals, notion of statistical convergence and ($ p_{nk} $ )-Ces\'aro summability in the space $ F^{2}(E,p,f,s) $ is also made.

Author Biographies

Anindita Basu

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India.

P. D. Srivastava

Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India.

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Published

2007-12-31

How to Cite

Basu, A., & Srivastava, P. D. (2007). Generalized vector valued double sequence space using modulus function. Tamkang Journal of Mathematics, 38(4), 347-366. https://doi.org/10.5556/j.tkjm.38.2007.69

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Section

Papers