scholarly journals On Ray's theorem for weak firmly nonexpansive mappings in Hilbert Spaces

2016 ◽  
Vol 12 (1) ◽  
pp. 5858-5861
Author(s):  
Tamer Nabil ◽  
Ahmed Hussein Soliman
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Firmly Nonexpansive Mapping ◽  
Firmly Nonexpansive ◽  
Firmly Nonexpansive Mappings

In this work, we introduce notions of generalized firmly nonexpansive (G-firmly non expansive) and fundamentally firmly nonexpansive (F-firmly nonexpansive) mappings and utilize to the same to prove Ray's theorem for G-firmly and F-firmly nonexpansive mappings in Hilbert Spaces. Our results extend the result due to F. Kohsaka [ Ray's theorem revisited: a fixed point free firmly nonexpansive mapping in Hilbert spaces, Journal of Inequalities and Applications (2015) 2015:86 ].

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.

Hybrid Iterative Approximation Method for a Fixed Point of Nonexpansive Mapping and Equilibrium Problem

2014 ◽  
Vol 568-570 ◽  
pp. 789-792
Author(s):  
Huang Xiang Zhang ◽  
Yan Hao ◽  
Ze Hong
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Iterative Approximation ◽  
Iterative Approximation Method

In this paper, a iterative method for approximating equilibrium problem and a fixed point of nonexpansive mappings was introduced in Hilbert spaces. And a strong convergence theorems of the iteration scheme was established. The results improve and extend the corresponding results of many others.

Modified CQ-Algorithms for G-Nonexpansive Mappings in Hilbert Spaces Involving Graphs

2020 ◽  
Vol 16 (01) ◽  
pp. 89-103
Author(s):  
W. Cholamjiak ◽  
D. Yambangwai ◽  
H. Dutta ◽  
H. A. Hammad
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Rate Of Convergence ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Iterative Schemes ◽  
Cq Method

In this paper, we introduce four new iterative schemes by modifying the CQ-method with Ishikawa and [Formula: see text]-iterations. The strong convergence theorems are given by the CQ-projection method with our modified iterations for obtaining a common fixed point of two [Formula: see text]-nonexpansive mappings in a Hilbert space with a directed graph. Finally, to compare the rate of convergence and support our main theorems, we give some numerical experiments.

scholarly journals Iterative Methods for Finding Solutions of a Class of Split Feasibility Problems over Fixed Point Sets in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1012
Author(s):  
Suthep Suantai ◽  
Narin Petrot ◽  
Montira Suwannaprapa
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Split Feasibility Problem ◽  
Inverse Image ◽  
Feasibility Problem ◽  
Point Sets ◽  
Fixed Point Set ◽  
Split Feasibility ◽  
Fixed Point Sets

We consider the split feasibility problem in Hilbert spaces when the hard constraint is common solutions of zeros of the sum of monotone operators and fixed point sets of a finite family of nonexpansive mappings, while the soft constraint is the inverse image of a fixed point set of a nonexpansive mapping. We introduce iterative algorithms for the weak and strong convergence theorems of the constructed sequences. Some numerical experiments of the introduced algorithm are also discussed.

scholarly journals Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals Fixed point theorems for nonexpansive mappings on nonconvex sets in UCED Banach spaces

2002 ◽  
Vol 31 (4) ◽  
pp. 251-257 ◽  
Author(s):  
Wei-Shih Du ◽  
Young-Ye Huang ◽  
Chi-Lin Yen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Compact Convex ◽  
Nonexpansive Mappings ◽  
Finite Union ◽  
Uniformly Convex ◽  
Weakly Compact ◽  
Nonconvex Sets ◽  
Firmly Nonexpansive ◽  
Asymptotically Regular

It is shown that every asymptotically regular orλ-firmly nonexpansive mappingT:C→Chas a fixed point wheneverCis a finite union of nonempty weakly compact convex subsets of a Banach spaceXwhich is uniformly convex in every direction. Furthermore, if{T i}i∈Iis any compatible family of strongly nonexpansive self-mappings on such aCand the graphs ofT i,i∈I, have a nonempty intersection, thenT i,i∈I, have a common fixed point inC.

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