Weak \(w^{2}\)-stability and data dependence of Mann iteration method in Hilbert spaces

  • Faik GürsoyEmail author
  • Abdul Rahim Khan
  • Müzeyyen Ertürk
  • Vatan Karakaya
Original Paper


We study a weaker and more natural notion of stability called weak \(w^{2}\)-stability to get an insight in the corresponding results obtained by Măruşter and Măruşter (J Comput Appl Math 276:110–116, 2015) and Wang (J Comput Appl Math 285:226–229, 2015). A data dependence result for fixed points of strongly demicontractive operators is also established. Some illustrative examples are given to validate results obtained herein.


Mann iteration Strongly demicontractive operator Data dependency Stability 

Mathematics Subject Classification

47H09 47H10 54H25 65J15 



The authors would like to thank the anonymous reviewers for their constructive comments to improve quality and presentation of the paper.


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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  • Faik Gürsoy
    • 1
    Email author
  • Abdul Rahim Khan
    • 2
  • Müzeyyen Ertürk
    • 1
  • Vatan Karakaya
    • 3
  1. 1.Department of MathematicsAdiyaman UniversityAdiyamanTurkey
  2. 2.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia
  3. 3.Department of Mathematical EngineeringYildiz Technical UniversityIstanbulTurkey

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