SHRINKING PROJECTION ALGORITHMS FOR THE SPLIT COMMON NULL POINT PROBLEM

2017 ◽  
Vol 96 (2) ◽  
pp. 299-306 ◽  
Author(s):  
VAHID DADASHI
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Convergence Theorem ◽  
Maximal Monotone ◽  
Null Point ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Projection Algorithms

We consider the split common null point problem in Hilbert space. We introduce and study a shrinking projection method for finding a solution using the resolvent of a maximal monotone operator and prove a strong convergence theorem for the algorithm.

scholarly journals Convergence theorems for finding the split common null point in Banach spaces

2017 ◽  
Vol 18 (2) ◽  
pp. 345 ◽  
Author(s):  
Suthep Suantai ◽  
Kittipong Srisap ◽  
Natthapong Naprang ◽  
Manatsawin Mamat ◽  
Vithoon Yundon ◽  
...  
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Null Point ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Convergence Theorems ◽  
Numerical Examples

<p>In this paper, we introduce a new iterative scheme for solving the split common null point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.</p>

scholarly journals A Modified Regularization Method for the Proximal Point Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shuang Wang
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Regularization Method ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Proximal Point ◽  
Weaker Conditions

Under some weaker conditions, we prove the strong convergence of the sequence generated by a modified regularization method of finding a zero for a maximal monotone operator in a Hilbert space. In addition, an example is also given in order to illustrate the effectiveness of our generalizations. The results presented in this paper can be viewed as the improvement, supplement, and extension of the corresponding results.

scholarly journals Iterative approximations with hybrid techniques for fixed points and equilibrium problems

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1997-2009
Author(s):  
Afrah Abdou ◽  
Badriah Alamri ◽  
Yeol Cho ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Strong Convergence Theorem ◽  
Point Problem ◽  
Hybrid Techniques ◽  
Contractive Mappings ◽  
Generalized Equilibrium

In this paper, we consider an iterative algorithm by using the shrinking projection method for solving the fixed point problem of the pseudo-contractive mappings and the generalized equilibrium problems. We prove some lemmas for our main result and a strong convergence theorem for the proposed algorithm.

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