Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

2008 ◽  
Vol 23 (3) ◽  
pp. 319-325 ◽  
Author(s):  
Li Wei ◽  
Yong-fu Su ◽  
Hai-yun Zhou
Keyword(s):  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Convergence Theorems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

scholarly journals Convergence Theorems for Maximal Monotone Operators, Weak Relatively Nonexpansive Mappings and Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Kamonrat Nammanee ◽  
Suthep Suantai ◽  
Prasit Cholamjiak
Keyword(s):  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Convex Banach Space ◽  
Point Problem ◽  
Convergence Theorems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We introduce hybrid-iterative schemes for solving a system of the zero-finding problems of maximal monotone operators, the equilibrium problem, and the fixed point problem of weak relatively nonexpansive mappings. We then prove, in a uniformly smooth and uniformly convex Banach space, strong convergence theorems by using a shrinking projection method. We finally apply the obtained results to a system of convex minimization problems.

scholarly journals Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chin-Tzong Pang ◽  
Eskandar Naraghirad ◽  
Ching-Feng Wen
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Maximal Monotone Operator ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Convergence Theorems ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature.

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