Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings

2009 ◽  
Vol 3 (4) ◽  
pp. 605-614 ◽  
Author(s):  
Sornsak Thianwan
Keyword(s):  
Strong Convergence ◽  
Hybrid Methods ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Monotone Mappings ◽  
Convergence Theorems ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals Δ-convergence theorems for inverse-strongly monotone mappings in CAT(0) spaces

2018 ◽  
Vol 19 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Sattar Alizadeh ◽  
◽  
Hossein Dehghan ◽  
Fridoun Moradlou ◽  
◽  
...  
Keyword(s):  
Monotone Mappings ◽  
Convergence Theorems ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings

scholarly journals Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1525-1536 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Convergence Theorems

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

scholarly journals A Viscosity Approximation Scheme for Finding Common Solutions of Mixed Equilibrium Problems, a Finite Family of Variational Inclusions, and Fixed Point Problems in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Baogui Xin
Keyword(s):  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Common Element ◽  
Monotone Mappings ◽  
Mixed Equilibrium Problems ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
Mixed Equilibrium

We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with set-valued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper improve and extend the main results of Plubtemg and Sripard and many others.

scholarly journals A New Iterative Method for the Set of Solutions of Equilibrium Problems and of Operator Equations with Inverse-Strongly Monotone Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jong Kyu Kim ◽  
Nguyen Buong ◽  
Jae Yull Sim
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Finite Family ◽  
Common Element ◽  
Monotone Mappings ◽  
Operator Equations ◽  
Strongly Monotone ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings ◽  
New Iterative Method

The purpose of the paper is to present a new iteration method for finding a common element for the set of solutions of equilibrium problems and of operator equations with a finite family ofλi-inverse-strongly monotone mappings in Hilbert spaces.

Sign in / Sign up

Export Citation Format

Share Document