Abstract

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

Keywords: Nonexpansive mapping; weak convergence; strong convergence; rate of convergence; iteration process.

MSC: 47H05, 49M05

Pages:  223$-$234     

Volume  66 ,  Issue  2 ,  2014