On iterative method for hierarchical fixed points problems and variational inequality problems

2013 ◽  
pp. 773-778
Author(s):  
Yeong-Cheng Liou
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Fixed Points ◽  
Variational Inequality Problems

scholarly journals Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2292
Author(s):  
Mujahid Abbas ◽  
Rizwan Anjum ◽  
Vasile Berinde
Keyword(s):  
Variational Inequality ◽  
Fixed Points ◽  
Variational Inequality Problems ◽  
Iterative Approximation ◽  
Iteration Methods ◽  
Split Feasibility ◽  
Iteration Processes

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

CONVERGENCE ANALYSIS ON HYBRID PROJECTION ALGORITHMS FOR EQUILIBRIUM PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS

2009 ◽  
Vol 14 (3) ◽  
pp. 335-351 ◽  
Author(s):  
Xiaolong Qin ◽  
Yeol Je Cho ◽  
Shin Min Kang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Method ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Variational Inequality Problems ◽  
Fixed Point Problems ◽  
Projection Algorithms

In this paper, we consider an iterative method for equilibrium problems, fixed point problems and variational inequality problems in the framework of Banach space. The results presented in this paper improve and extend the corresponding results announced by many others.

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