The hybrid projection algorithm for finding the common fixed points of nonexpansive mappings and the zeroes of maximal monotone operators in Banach spaces

Optimization ◽  
2012 ◽  
Vol 63 (9) ◽  
pp. 1319-1338 ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam ◽  
Preedaporn Kanjanasamranwong
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Fixed Points ◽  
Projection Algorithm ◽  
The Common ◽  
Hybrid Projection Algorithm

scholarly journals Hybrid Projection Algorithm for Two Countable Families of Hemirelatively Nonexpansive Mappings and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zi-Ming Wang ◽  
Poom Kumam
Keyword(s):  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Projection Algorithm ◽  
Uniformly Convex ◽  
Uniformly Smooth ◽  
Convex Feasibility ◽  
Hybrid Projection Algorithm

Two countable families of hemirelatively nonexpansive mappings are considered based on a hybrid projection algorithm. Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yaqin Wang
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Fixed Points ◽  
Generalized Mixed Equilibrium Problem ◽  
Common Element ◽  
Strong Convergence Theorem

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.

scholarly journals Retraction method in fixed point theory for monotone nonexpansive mappings

2016 ◽  
Vol 32 (3) ◽  
pp. 271-276
Author(s):  
M. R. ALFURAIDAN ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Point Theory ◽  
Common Fixed Points ◽  
The Common ◽  
Nonexpansive Retract

In this paper we study the properties of the common fixed points set of a commuting family of monotone nonexpansive mappings in Banach spaces endowed with a graph. In particular, we prove that under certain conditions, this set is a monotone nonexpansive retract.

Sign in / Sign up

Export Citation Format

Share Document