scholarly journals Strong convergence theorems for coordinatewise negatively associated random vectors in Hilbert space

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Xiang Huang ◽  
Yongfeng Wu
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Random Vectors ◽  
Convergence Theorems ◽  
Negatively Associated

scholarly journals Strong Convergence Theorems for a Pair of Strictly Pseudononspreading Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bin-Chao Deng ◽  
Tong Chen
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Real Hilbert Space ◽  
Convergence Theorems ◽  
Mild Conditions ◽  
Strongly Monotone

LetHbe a real Hilbert space. LetT1,T2:H→Hbek1-,k2-strictly pseudononspreading mappings; letαnandβnbe two real sequences in (0,1). For givenx0∈H, the sequencexnis generated iteratively byxn+1=βnxn+1-βnTw1αnγfxn+I-μαnBTw2xn,∀n∈N, whereTwi=1−wiI+wiTiwithi=1,2andB:H→His strongly monotone and Lipschitzian. Under some mild conditions on parametersαnandβn, we prove that the sequencexnconverges strongly to the setFixT1∩FixT2of fixed points of a pair of strictly pseudononspreading mappingsT1andT2.

scholarly journals Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
P. Cholamjiak ◽  
W. Cholamjiak ◽  
S. Suantai
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Equilibrium Problems ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Viscosity Approximation Methods

AbstractIn this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

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 Strong Convergence Theorems for Maximal Monotone Operators with Nonspreading Mappings in a Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjie Liu ◽  
Junqing Wang ◽  
Qiansheng Feng
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Mapping ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Element ◽  
Convergence Theorems ◽  
Nonspreading Mappings

We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mappingTand the solution sets of zero of a maximal monotone mapping and anα-inverse strongly monotone mapping in a Hilbert space. Manaka and Takahashi (2011) proved weak convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space; there we introduced new iterative algorithms and got some strong convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space.

scholarly journals Strong Convergence Theorems for Equilibrium Problems andk-Strict Pseudocontractions in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dao-Jun Wen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Common Element ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed point of a finite family ofk-strictly pseudo-contractive nonself-mappings. Strong convergence theorems are established in a real Hilbert space under some suitable conditions. Our theorems presented in this paper improve and extend the corresponding results announced by many others.

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