Approximation of Common Fixed Points and the Solution of Image Recovery Problem
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In the present paper, we study one step iterative scheme to approximate common fixed points of two generalized non-expansive mappings in uniformly convex Banach spaces and using the same scheme we prove some weak and strong convergence results for such mappings. Further, we establish some weak and strong convergence results for a finite family of generalized non-expansive mappings to approximate common fixed points using proposed algorithm in uniformly convex Banach spaces. As an application, we apply our main result to approximate the solution of image recovery problem in Banach space setting. To support our results we present some illustrative numerical examples. Our results are new and generalize several relevant results in the literature.
KeywordsGeneralized non-expansive mappings common fixed points one step iterative scheme weak and strong convergence results uniformly convex Banach spaces image recovery
Mathematics Subject Classification47H09 47H10
The authors are grateful to the anonymous referee for his valuable comments which improve the paper. The second author would like to thank Council of Scientific and Industrial Research, Government of India for SRF (09/112(0536)/2016-EMR-I).
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