scholarly journals Convergence theorems for finding zero points of maximal monotone operators and equilibrium problems in Banach spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam ◽  
Yeol Je Cho
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convergence Theorems ◽  
Zero Points

scholarly journals Strong Convergence Theorems for Maximal Monotone Operators, Fixed-Point Problems, and Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Huan-chun Wu ◽  
Cao-zong Cheng ◽  
De-ning Qu
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Optimization Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Element ◽  
Convergence Theorems ◽  
New Iterative Method

We present a new iterative method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions to an equilibrium problem, and the set of zeros of the sum of maximal monotone operators and prove the strong convergence theorems in the Hilbert spaces. We also apply our results to variational inequality and optimization problems.

scholarly journals New Convergence Theorems for Maximal Monotone Operators in Banach Spaces

2021 ◽  
Vol 15 ◽  
pp. 8-13
Author(s):  
Siwaporn Saewan
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convex Minimization ◽  
Variational Inequality Problems ◽  
Convergence Theorems

The purpose of this paper is to introduce a new hybrid iterative scheme for resolvents of maximal monotone operators in Banach spaces by using the notion of generalized fprojection. Next, we apply this result to the convex minimization and variational inequality problems in Banach spaces. The results presented in this paper improve and extend important recent results in the literature.

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