Mann type iterative methods for finding a common solution of split feasibility and fixed point problems

Mann type iterative methods for finding a common solution of split feasibility and fixed point... The purpose of this paper is to study and analyze three different kinds of Mann type iterative methods for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in the setting of infinite-dimensional Hilbert spaces. By combining Mann’s iterative method and the extragradient method, we first propose Mann type extragradient-like algorithm for finding an element of the set $${{{\rm Fix}}(S) \cap \Gamma}$$ ; moreover, we derive the weak convergence of the proposed algorithm under appropriate conditions. Second, we combine Mann’s iterative method and the viscosity approximation method to introduce Mann type viscosity algorithm for finding an element of the $${{{\rm Fix}}(S)\cap \Gamma}$$ ; moreover, we derive the strong convergence of the sequences generated by the proposed algorithm to an element of set $${{{\rm Fix}}(S) \cap \Gamma}$$ under mild conditions. Finally, by combining Mann’s iterative method and the relaxed CQ method, we introduce Mann type relaxed CQ algorithm for finding an element of the set $${{{\rm Fix}}(S)\cap \Gamma}$$ . We also establish a weak convergence result for the sequences generated by the proposed Mann type relaxed CQ algorithm under appropriate assumptions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Mann type iterative methods for finding a common solution of split feasibility and fixed point problems

Loading next page...
 
/lp/springer_journal/mann-type-iterative-methods-for-finding-a-common-solution-of-split-eOnvBEKqOz
Publisher
SP Birkhäuser Verlag Basel
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Operator Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics; Potential Theory; Fourier Analysis
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0174-8
Publisher site
See Article on Publisher Site

References

  • On relaxed viscosity iterative methods for variational inequalities in Banach spaces
    Ceng, L.C.; Ansari, Q.H.; Yao, J.C.

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

$49/month

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.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial