Advanced search
Publication Cover
Numerical Functional Analysis and Optimization Volume 33, 2012 - Issue 11
Submit an article Journal homepage
173
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Viscosity Approximation Methods for Multivalued Mappings in Banach Spaces

Yunan Cui Department of Mathematics, Harbin University of Science and Technology, Harbin, Heilongjiang, P. R. China
,
Zuo Zhan Fei Department of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou Chongqing, P. R. China
&
Henryk Hudzik Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, PolandCorrespondence[email protected]
Pages 1288-1303 | Received 12 May 2011, Accepted 22 Apr 2012, Published online: 10 Oct 2012

REFERENCES

  • N. A. Assad and W. A. Kirk ( 1972 ). Fixed point theorems for set-valued mappings ofcontractive type . Pacific J. Math. 43 : 553 – 562 .
  • D. Dowling and W. A. Kirk ( 1977 ). Fixed point theorems for set-valued mappings inmetric and Banach spaces . Math. Japonicae 22 : 99 – 112 .
  • J. P. Gossez and E. LamiDozo ( 1972 ). Some geometric properties related to the fixedpoint theory for nonexpansive mappings . Pacific J. Math. 40 : 565 – 573 .
  • W. A. Kirk ( 2003 ). Transfinite methods in metric fixed point theorey . Abstract and Applied Analysis 5 : 311 – 324 .
  • T. C. Lim ( 1974 ). A fixed point theorem for multivalued nonexpansive mappings in auniformly convex Banach space . Bull. Amer. Math. Soc. 80 : 1123 – 1126 .
  • T. C. Lim ( 1976 ). Remarks on some fixed point theorems . Proc. Amer. Math. Soc. 60 : 179 – 182 .
  • L. S. Liu ( 1995 ). Ishikawa and Mann iterative processes with errors for nonlinearstrongly accretive mappings in Banach spaces . J. Math. Anal. Appl. 194 : 114 – 125 .
  • C. H. Morales and J. S. Jung ( 2000 ). Convergence of paths for pseudo-contractivemappings in Banach spaces . Proc. Amer. Math. Soc. 128 : 3411 – 3419 .
  • A. Moudafi ( 2000 ). Viscosity approximation methods for fixed point problems . J. Math. Anal. Appl. 241 : 46 – 55 .
  • S. B. Nadler , Jr. ( 1969 ). Multi-valued contraction mappings . Pacific J. Math. 30 : 475 – 487 .
  • Z. Opial ( 1967 ). Weak convergence of the sequence of successive approximations fornonexpansive mappings . Bull. Amer. Math. Soc. 73 : 591 – 597 .
  • D. R. Sahu (1999). Strong convergence theorems for nonexpansive type and non-selfmulti-valued mappings. Nonlinear Anal. 37:401–407.
  • Y. Song and R. Chen ( 2006 ). Viscosity approximation methods for nonexpansivenonself-mappings . J. Math. Anal. Appl. 321 : 316 – 326 .
  • T. Suzuki ( 2005 ). Strong convergence theorems for infinite families of nonexpansivemappings in general Banach spaces . Fixed Point Theory Appl. 1 : 103 – 123 .
  • H. K. Xu ( 2001 ). Multivalued nonexpansive mappings in Banach spaces . NonlinearAnal. 43 : 693 – 706 .
  • H. K. Xu (to appear) . A strong convergence theorem for nonexpansive mappings . J. Math. Anal. Appl.
  • H. K. Xu ( 2004 ). Viscosity approximation methods for nonexpansive mappings . J. Math. Anal. Appl. 298 : 279 – 291 .
  • K. Yanagi ( 1980 ). On some fixed point theorems for multivalued mappings . Pacific J. Math. 87 : 233 – 240 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.