scholarly journals Two New Iterative Methods for a Countable Family of Nonexpansive Mappings in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Shuang Wang ◽  
Changsong Hu
Keyword(s):  
Iterative Methods ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Countable Family

scholarly journals Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 936 ◽  
Author(s):  
Suthep Suantai ◽  
Mana Donganont ◽  
Watcharaporn Cholamjiak
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Directed Graph ◽  
Hilbert Spaces ◽  
Hybrid Methods ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Countable Family

In this paper, we introduce the iterative scheme for finding a common fixed point of a countable family of G-nonexpansive mappings by the shrinking projection method which generalizes Takahashi Takeuchi and Kubota’s theorem in a Hilbert space with a directed graph. Simultaneously, we give examples and numerical results for supporting our main theorems and compare the rate of convergence of some examples under the same conditions.

scholarly journals Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shuang Wang
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family

We propose a general composite iterative method for computing common fixed points of a countable family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and complement the corresponding ones announced by many others.

scholarly journals An Iterative Shrinking Metricf-Projection Method for Finding a Common Fixed Point of a Closed and Quasi-Strictf-Pseudocontraction and a Countable Family of Firmly Nonexpansive Mappings and Applications in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Kasamsuk Ungchittrakool ◽  
Duangkamon Kumtaeng
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Countable Family ◽  
Common Solution ◽  
Firmly Nonexpansive ◽  
Generalized Mixed Equilibrium ◽  
Firmly Nonexpansive Mappings

We create some new ideas of mappings called quasi-strictf-pseudocontractions. Moreover, we also find the significant inequality related to such mappings and firmly nonexpansive mappings within the framework of Hilbert spaces. By using the ideas of metricf-projection, we propose an iterative shrinking metricf-projection method for finding a common fixed point of a quasi-strictf-pseudocontraction and a countable family of firmly nonexpansive mappings. In addition, we provide some applications of the main theorem to find a common solution of fixed point problems and generalized mixed equilibrium problems as well as other related results.

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