Numerical Algorithms

, Volume 81, Issue 3, pp 1129–1148 | Cite as

Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process

  • H. PiriEmail author
  • B. Daraby
  • S. Rahrovi
  • M. Ghasemi
Original Paper


In this paper, we introduce a new iterative scheme to approximate fixed point of generalized α-nonexpansive mappings and then, we prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. At the end, by using an example for generalized α-nonexpansive mappings, we compare the convergence behavior of new iterative process with other iterative processes.


Uniformly convex Banach space Convergence theorem Generalized α-nonexpansive mapping Opial’s property 

Mathematics Subject Classification (2010)

Primary: 47H05 Secondary: 47H09, 47H20 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BonabBonabIran
  2. 2.Department of MathematicsUniversity of MaraghehMaraghehIran

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