scholarly journals Weak Convergence Theorem for Finding Fixed Points and Solution of Split Feasibility and Systems of Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Kamonrat Sombut ◽  
Somyot Plubtieng
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Split Feasibility Problems ◽  
Mild Conditions ◽  
Weak Convergence Theorem ◽  
Split Feasibility

The purpose of this paper is to introduce an iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and the solution of split feasibility problems (SFP) and systems of equilibrium problems (SEP) in Hilbert spaces. We prove that the sequences generated by the proposed algorithm converge weakly to a common element of the fixed points set of quasi-nonexpansive mappings and the solution of split feasibility problems and systems of equilibrium problems under mild conditions. Our main result improves and extends the recent ones announced by Ceng et al. (2012) and many others.

scholarly journals Iterative methods for generalized split feasibility problems in Banach spaces

2017 ◽  
Vol 33 (1) ◽  
pp. 09-26
Author(s):  
QAMRUL HASAN ANSARI ◽  
◽  
AISHA REHAN ◽  
◽  
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Split Feasibility Problems ◽  
Convergence Results ◽  
Split Feasibility

Inspired by the recent work of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, Set-Valued Var. Anal., 23 (2015), 205–221], in this paper, we study generalized split feasibility problems (GSFPs) in the setting of Banach spaces. We propose iterative algorithms to compute the approximate solutions of such problems. The weak convergence of the sequence generated by the proposed algorithms is studied. As applications, we derive some algorithms and convergence results for some problems from nonlinear analysis, namely, split feasibility problems, equilibrium problems, etc. Our results generalize several known results in the literature including the results of Takahashi et al. [W. Takahashi, H.-K. Xu and J.-C. Yao, Iterative methods for generalized split feasibility problems in Hilbert spaces, SetValued Var. Anal., 23 (2015), 205–221].

scholarly journals Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Nimit Nimana
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Shrinking Projection Method ◽  
Generalized Equilibrium

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

Strong and weak convergence theorems for fixed points of a class of nonlinear mappings

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Changqun Wu ◽  
Zhiqiang Wei ◽  
Yu Li
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Weak Convergence Theorem

AbstractIn this paper, the class of total asymptotically nonexpansive mappings is considered. A weak convergence theorem of Mann-type iterative algorithm is established. Hybrid projection methods are considered for the class of total asymptotically nonexpansive mappings. Strong convergence theorems are also established in the framework of Hilbert spaces.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family ofki-Strictly Pseudocontractive Mapping in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Haitao Che ◽  
Meixia Li ◽  
Xintian Pan
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Element ◽  
Strictly Pseudocontractive Mapping ◽  
Pseudocontractive Mappings ◽  
Definition Of ◽  
Strictly Pseudocontractive Mappings

We first extend the definition of Wnfrom an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family ofki-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

An Iterative Method for Mixed Equilibrium Problems and Fixed Points

2012 ◽  
Vol 263-266 ◽  
pp. 283-286 ◽  
Author(s):  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Engineering Calculation ◽  
Common Element ◽  
Rounding Errors ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

Fixed point computation plays an important role in the field of engineering calculation. Rounding errors often cause no convergence for iteration sequence or results distortion in many fixed point iterative method. In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of olutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

An Iterative Method for Equilibrium Problems and Fixed Point Problems

2014 ◽  
Vol 513-517 ◽  
pp. 382-385
Author(s):  
Chen Min ◽  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Common Element ◽  
Mixed Equilibrium Problems

In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

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