A new faster iteration process applied to constrained minimization and feasibility problems

Authors

  • Mujahid Abbas M. Abbas, Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa and Department of Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan Author
  • Talat Nazir T. Nazir, Department of Mathematics, COMSATS Institute of Information Technology, 22060 Abbottabad, Pakistan Author

Keywords:

Nonexpansive mapping, weak convergence, strong convergence, rate of convergence, iteration process

Subjects:

47H05, 49M05

Abstract

We introduce a new iteration processand prove that it is faster than all of Picard, Mann and Agarwal et al\.processes. We support analytic proof by a numerical example. Our processis independent of all three processes just mentioned. We also prove someweak and strong convergence theorems for two nonexpansive mappings.Moreover, we apply our results to find solutions of constrained minimizationproblems and feasibility problems.

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Published

2014-04-15

Issue

Vol. 66 No. 2 (2014): Vol. 66, Issue 2

Section

Articles

License

Copyright (c) 2014 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.