scholarly journals The shrinking projection method for a finite family of demimetric mappings with variational inequality problems in a Hilbert space

2018 ◽  
Vol 19 (1) ◽  
pp. 407-420 ◽  
Author(s):  
Wataru Takahashi ◽  
◽  
Ching-Feng Wen ◽  
Jen-Chih Yao ◽  
◽  
...  
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Projection Method ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Shrinking Projection Method

scholarly journals A Strong Convergence Theorem under a New Shrinking Projection Method for Finite Families of Nonlinear Mappings in a Hilbert Space

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 435
Author(s):  
Wataru Takahashi
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Projection Method ◽  
Monotone Mapping ◽  
Maximal Monotone ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Shrinking Projection Method ◽  
Zero Points

In this paper, using a new shrinking projection method, we deal with the strong convergence for finding a common point of the sets of zero points of a maximal monotone mapping, common fixed points of a finite family of demimetric mappings and common zero points of a finite family of inverse strongly monotone mappings in a Hilbert space. Using this result, we get well-known and new strong convergence theorems in a Hilbert space.

scholarly journals PARALLEL EXTRAGRADIENT-PROXIMAL METHODS FOR SPLIT EQUILIBRIUM PROBLEMS

2016 ◽  
Vol 21 (4) ◽  
pp. 478-501 ◽  
Author(s):  
Dang Van Hieu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Projection Method ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Proximal Methods ◽  
Proximal Method ◽  
Weak And Strong Convergence ◽  
Split Variational Inequality

In this paper, we introduce two parallel extragradient-proximal methods for solving split equilibrium problems. The algorithms combine the extragradient method, the proximal method and the shrinking projection method. The weak and strong convergence theorems for iterative sequences generated by the algorithms are established under widely used assumptions for equilibrium bifunctions. We also present an application to split variational inequality problems and a numerical example to illustrate the convergence of the proposed algorithms.

scholarly journals An Iterative Method for Solving Split Monotone Variational Inclusion Problems and Finite Family of Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Wanna Sriprad ◽  
Somnuk Srisawat
Keyword(s):  
Variational Inequality ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Variational Inequality Problems ◽  
Variational Inclusion ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Convex Minimization Problems

The purpose of this paper is to study the convergence analysis of an intermixed algorithm for finding the common element of the set of solutions of split monotone variational inclusion problem (SMIV) and the set of a finite family of variational inequality problems. Under the suitable assumption, a strong convergence theorem has been proved in the framework of a real Hilbert space. In addition, by using our result, we obtain some additional results involving split convex minimization problems (SCMPs) and split feasibility problems (SFPs). Also, we give some numerical examples for supporting our main theorem.

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