Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization
by
Gabriela Ioana Usurelu 1
and 
Mihai Postolache 1,2,3,*
Gabriela Ioana Usurelu 1 and Mihai Postolache 1,2,3,*
1
Department of Mathematics and Informatics, University Politehnica of Bucharest, 060042 Bucharest, Romania
2
Center for General Education, China Medical University, Taichung 40402, Taiwan
3
Romanian Academy, Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1441; https://doi.org/10.3390/sym11121441
Received: 22 October 2019 / Revised: 14 November 2019 / Accepted: 21 November 2019 / Published: 23 November 2019
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence.
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Keywords:
Suzuki mapping; three-step iteration; convergence; Opial’s property
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MDPI and ACS Style
Usurelu, G.I.; Postolache, M. Convergence Analysis for a Three-Step Thakur Iteration for Suzuki-Type Nonexpansive Mappings with Visualization. Symmetry 2019, 11, 1441.
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