On The Paranormed Spaces of Regularly Convergent Double Sequences

On The Paranormed Spaces of Regularly Convergent Double Sequences In Hardy (Proc Camb Philos 19:86–95, 1916), Hardy defined the normed spaces $$\mathcal {C}_{r}$$ C r and $$\mathcal {C}_{r0}$$ C r 0 of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations). In this paper, we extend these spaces to the paranormed spaces $$\mathcal {C}_{r}(t)$$ C r ( t ) and $$\mathcal {C}_{r0}(t)$$ C r 0 ( t ) . Also, we define the paranormed spaces $$\mathcal {C}_{tr}(t)$$ C t r ( t ) and $$\mathcal {C}_{tr0}(t)$$ C t r 0 ( t ) of all totally regularly convergent and totally regularly null double sequences. We examine some topological properties of these spaces and determine their alpha-, beta- and gamma-duals. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

On The Paranormed Spaces of Regularly Convergent Double Sequences

Loading next page...
Springer International Publishing
Copyright © 2017 by Springer International Publishing
Mathematics; Mathematics, general
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial