scholarly journals Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Minimum Norm ◽  
Practical Applications ◽  
Fixed Point Computation ◽  
The Common ◽  
Special Case

Fixed point (especially, the minimum norm fixed point) computation is an interesting topic due to its practical applications in natural science. The purpose of the paper is devoted to finding the common fixed points of an infinite family of nonexpansive mappings. We introduce an iterative algorithm and prove that suggested scheme converges strongly to the common fixed points of an infinite family of nonexpansive mappings under some mild conditions. As a special case, we can find the minimum norm common fixed point of an infinite family of nonexpansive mappings.

scholarly journals Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yaqin Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Viscosity Method ◽  
Hierarchical Fixed Point ◽  
The Common ◽  
Hierarchical Fixed Point Problems

A viscosity method for hierarchical fixed point problems is presented to solve variational inequalities, where the involved mappings are nonexpansive nonself-mappings. Solutions are sought in the set of the common fixed points of an infinite family of nonexpansive nonself-mappings. The results generalize and improve the recent results announced by many other authors.

scholarly journals Retraction method in fixed point theory for monotone nonexpansive mappings

2016 ◽  
Vol 32 (3) ◽  
pp. 271-276
Author(s):  
M. R. ALFURAIDAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Common Fixed Points ◽  
The Common ◽  
Nonexpansive Retract

In this paper we study the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings in Banach spaces endowed with a graph. In particular, we prove that under certain conditions, this set is a monotone nonexpansive retract.

Approximation of fixed point of accretive operators based on a Halpern-Type iterative method

2017 ◽  
Vol 26 (3) ◽  
pp. 263-274
Author(s):  
KADRI DOGAN ◽  
◽  
VATAN KARAKAYA ◽  
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Convergence Result ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Iterative Sequence ◽  
Uniformly Convex ◽  
Accretive Operators ◽  
The Common

In this study, we introduce a new iterative processes to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. Also we prove that this process to approximate zeros of an infinite family of accretive operators and we obtain a strong convergence result for these operators. Our results improve and generalize many known results in the current literature.

scholarly journals Iterative Algorithm for Common Fixed Points of Infinite Family of Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Songnian He ◽  
Jun Guo
Keyword(s):  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Duality Mapping ◽  
Normalized Duality Mapping ◽  
Uniformly Smooth ◽  
Computational Work

LetCbe a nonempty closed convex subset of a real uniformly smooth Banach spaceX,{Tk}k=1∞:C→Can infinite family of nonexpansive mappings with the nonempty set of common fixed points⋂k=1∞Fix⁡(Tk), andf:C→Ca contraction. We introduce an explicit iterative algorithmxn+1=αnf(xn)+(1-αn)Lnxn, whereLn=∑k=1n(ωk/sn)Tk,Sn=∑k=1nωk,  andwk>0with∑k=1∞ωk=1. Under certain appropriate conditions on{αn}, we prove that{xn}converges strongly to a common fixed pointx*of{Tk}k=1∞, which solves the following variational inequality:〈x*-f(x*),J(x*-p)〉≤0,    p∈⋂k=1∞Fix(Tk), whereJis the (normalized) duality mapping ofX. This algorithm is brief and needs less computational work, since it does not involveW-mapping.

scholarly journals Strong Convergence Theorems for Common Fixed Points of an Infinite Family of Asymptotically Nonexpansive Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Yuanheng Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Real Banach Space ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Uniformly Gâteaux Differentiable Norm ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Differentiable Norm

In the framework of a real Banach space with uniformly Gateaux differentiable norm, some new viscosity iterative sequences{xn}are introduced for an infinite family of asymptotically nonexpansive mappingsTii=1∞in this paper. Under some appropriate conditions, we prove that the iterative sequences{xn}converge strongly to a common fixed point of the mappingsTii=1∞, which is also a solution of a variational inequality. Our results extend and improve some recent results of other authors.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals Finding common fixed points of nonexpansive mappings by iteration

2000 ◽  
Vol 62 (2) ◽  
pp. 307-310 ◽  
Author(s):  
B. E. Rhoades
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Finite Set

In this paper it is shown that a particular iteration scheme converges weakly to a common fixed point of a finite set of nonexpansive mappings. This result is an improvement of two related theorems in the literature.

scholarly journals Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yeong-Cheng Liou
Keyword(s):  
Fixed Point ◽  
Inverse Problems ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Minimum Norm ◽  
Pseudocontractive Mappings ◽  
Special Cases ◽  
Implicit And Explicit ◽  
Strictly Pseudocontractive Mappings

It is known that strictly pseudocontractive mappings have more powerful applications than nonexpansive mappings in solving inverse problems. In this paper, we devote to study computing the fixed points of strictly pseudocontractive mappings by the iterations. Two iterative methods (one implicit and another explicit) for finding the fixed point of strictly pseudocontractive mappings have been constructed in Hilbert spaces. As special cases, we can use these two methods to find the minimum norm fixed point of strictly pseudocontractive mappings.

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