scholarly journals Convergence theorem for I-asymptotically quasi-nonexpansive mapping in Hilbert space

2007 ◽  
Vol 329 (2) ◽  
pp. 759-765 ◽  
Author(s):  
Seyit Temir ◽  
Ozlem Gul
Keyword(s):  
Hilbert Space ◽  
Nonexpansive Mapping ◽  
Convergence Theorem

scholarly journals Hybrid subgradient algorithm for equilibrium and fixed point problems by approximation of nonexpansive mapping

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1721-1729
Author(s):  
Seyed Aleomraninejad ◽  
Kanokwan Sitthithakerngkiet ◽  
Poom Kumam
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Expansive Mapping ◽  
Subgradient Algorithm

In this paper anew algorithm considered on a real Hilbert space for finding acommonpoint in the solution set of a class of pseudomonotone equilibrium problem and the set of fixed points of nonexpansive mappings. We produce this algorithm by mappings Tk that are approximations of non-expansive mapping T. The strong convergence theorem of the proposed algorithms is investigated. Our results generalize some recent results in the literature.

An L 2 convergence theorem for random affine mappings

1995 ◽  
Vol 32 (01) ◽  
pp. 183-192 ◽  
Author(s):  
Robert M. Burton ◽  
Uwe Rösler
Keyword(s):  
Hilbert Space ◽  
Lyapunov Exponent ◽  
Bilinear Form ◽  
Convergence Theorem ◽  
Convergence In Distribution ◽  
Wasserstein Metric ◽  
Affine Mappings ◽  
Affine Maps ◽  
Second Moments ◽  
Contraction Condition

We consider the composition of random i.i.d. affine maps of a Hilbert space to itself. We show convergence of thenth composition of these maps in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger and easier to check. In addition, our condition allows us to conclude convergence of second moments as well as convergence in distribution.

scholarly journals Hybrid Projection Algorithm for a New General System of Variational Inequalities in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-22
Author(s):  
S. Imnang
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Real Hilbert Space ◽  
General System ◽  
Projection Algorithm ◽  
Common Element ◽  
System Of Variational Inequalities ◽  
Demiclosedness Principle ◽  
Hybrid Projection Algorithm

A new general system of variational inequalities in a real Hilbert space is introduced and studied. The solution of this system is shown to be a fixed point of a nonexpansive mapping. We also introduce a hybrid projection algorithm for finding a common element of the set of solutions of a new general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Several strong convergence theorems of the proposed hybrid projection algorithm are established by using the demiclosedness principle. Our results extend and improve recent results announced by many others.

scholarly journals Existence and Approximation of Attractive Points of the Widely More Generalized Hybrid Mappings in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Sy-Ming Guu ◽  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Mean Convergence ◽  
Nonspreading Mappings ◽  
Weak Convergence Theorem ◽  
Attractive Point ◽  
Nonlinear Mappings

We study the widely more generalized hybrid mappings which have been proposed to unify several well-known nonlinear mappings including the nonexpansive mappings, nonspreading mappings, hybrid mappings, and generalized hybrid mappings. Without the convexity assumption, we will establish the existence theorem and mean convergence theorem for attractive point of the widely more generalized hybrid mappings in a Hilbert space. Moreover, we prove a weak convergence theorem of Mann’s type and a strong convergence theorem of Shimizu and Takahashi’s type for such a wide class of nonlinear mappings in a Hilbert space. Our results can be viewed as a generalization of Kocourek, Takahashi and Yao, and Hojo and Takahashi where they studied the generalized hybrid mappings.

scholarly journals Fixed Point Theorems for an Elastic Nonlinear Mapping in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Hiroko Manaka
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Duality Mapping ◽  
Nonlinear Mapping ◽  
Normalized Duality Mapping ◽  
Strongly Nonexpansive Mapping ◽  
Weak Convergence Theorem

LetEbe a smooth Banach space with a norm·. LetV(x,y)=x2+y2-2 x,Jyfor anyx,y∈E, where·,·stands for the duality pair andJis the normalized duality mapping. We define aV-strongly nonexpansive mapping byV(·,·). This nonlinear mapping is nonexpansive in a Hilbert space. However, we show that there exists aV-strongly nonexpansive mapping with fixed points which is not nonexpansive in a Banach space. In this paper, we show a weak convergence theorem and strong convergence theorems for fixed points of this elastic nonlinear mapping and give the existence theorem.

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