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Ishikawa iterative process for hemicontractive multi-valued non-self mappings in CAT(0) spaces

  • Abebe R. Tufa
  • H. ZegeyeEmail author
Original Paper
  • 98 Downloads

Abstract

Our purpose in this paper is to construct Ishikawa iterative scheme formulti-valued non-self mappings in CAT(0) spaces. Then we obtain strong convergence of the scheme to a fixed point of multi-valued hemicontractive non-self mapping in a complete CAT(0) space. In addition, we define pseudocontractive mapping in CAT(0) spaces and show that a pseudocontractive mapping T with \(F(T)\not =\emptyset \) and \(Tp=\{p\}, \forall p\in F(T)\) is hemicontractive mapping. Furthermore, we give an example of hemicontractive mapping which is not pseudocontarctive to show that the converse is not necessarily true. Our theorems improve and unify most of the results in the literature.

Keywords

CAT(0) space Hemicontractive mappings Fixed points Hausdorff distance Multi-valued mapping Non-self mappings 

Mathematics Subject Classification

Primary 37C25 47H09 Secondary 47H04 

Notes

Acknowledgements

The authors are grateful to the referees and the editor for their careful observation and valuable comments and suggestions which lead the paper to its present form.

Compliance with ethical standards

Funding

A. R. Tufa is supported by IMU Break Out Fellowship Program through TWAS and partially supported by Bahir Dar University, Ethiopia and the Simons Foundation based at Botswana International University of Science and Technology.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BotswanaGaboroneBotswana
  2. 2.Department of MathematicsBahir Dar UniversityBahir DarEthiopia
  3. 3.Department of MathematicsBotswana International University of Science and TechnologyPalapyeBotswana

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