scholarly journals Weak convergence theorems of a hybrid algorithm in Hilbert spaces

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Yan Hao
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Convergence Theorems

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.

Strong and weak convergence theorems for general mixed equilibrium problems and general variational inequality problems and fixed point problems for two nonexpansive semigroups in Hilbert spaces

2021 ◽  
pp. 152-160
Author(s):  
Baoshuai Zhang ◽  
◽  
Ying Tian ◽  
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Common Element ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Nonexpansive Semigroups ◽  
General Variational Inequality ◽  
Mixed Equilibrium

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and the set of solutions of a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results announced by many others.

scholarly journals Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Juguo Su ◽  
Yuchao Tang ◽  
Liwei Liu
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Hybrid Algorithm ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Iteration Methods ◽  
Mann’S Iteration

The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.

scholarly journals WEAK CONVERGENCE OF COMPOUND PROBABILITY MEASURES ON UNIFORM SPACES

1999 ◽  
Vol 30 (4) ◽  
pp. 271-288
Author(s):  
JUN KAWABE
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Transition Probabilities ◽  
Uniform Space ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Convergence Theorems ◽  
Covariance Functions ◽  
Compound Probability

We obtain a convergence theorem of compound probability measures on a uniform space for a net of uniformly equicontinuous transition probabilities. This theorem contains convergence theorems of product or convolution measures. We also show that for Gaussian transition probabilities on a Hilbert spaces, our assumptions in the convergence theorem can be expressed in terms of mean and covariance functions.

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