Approximating fixed points of generalized α-nonexpansive mappings in Banach spaces by new faster iteration process
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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.
KeywordsUniformly 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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- 10.Shahin, F., Adrian, G., Mihai, P., Shahram, R.: A comparative study on the convergence rate of some iteration methods involving contractive mappings. Fixed Point Theory Appl, pp. 24 (2015)Google Scholar