Iterative approximation method for various nonlinear mappings and equilibrium problems with numerical example

2016 ◽  
Vol 111 (1) ◽  
pp. 65-88 ◽  
Author(s):  
Wongvisarut Khuangsatung ◽  
Atid Kangtunyakarn
Keyword(s):  
Approximation Method ◽  
Equilibrium Problems ◽  
Iterative Approximation ◽  
Numerical Example ◽  
Iterative Approximation Method ◽  
Nonlinear Mappings

scholarly journals A strong convergence theorem for a zero of the sum of a finite family of maximally monotone mappings

2020 ◽  
Vol 53 (1) ◽  
pp. 152-166 ◽  
Author(s):  
Getahun B. Wega ◽  
Habtu Zegeye ◽  
Oganeditse A. Boikanyo
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Convergence Theorem ◽  
Finite Family ◽  
Strong Convergence Theorem ◽  
Monotone Mappings ◽  
Important Class ◽  
Numerical Example ◽  
Minimization Problems ◽  
Nonlinear Mappings

AbstractThe purpose of this article is to study the method of approximation for zeros of the sum of a finite family of maximally monotone mappings and prove strong convergence of the proposed approximation method under suitable conditions. The method of proof is of independent interest. In addition, we give some applications to the minimization problems and provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

scholarly journals An Iterative Approximation Method for a Common Fixed Point of Two Pseudocontractive Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Approximation Method ◽  
Finite Family ◽  
Convex Minimization Problem ◽  
Iterative Approximation ◽  
Pseudocontractive Mappings ◽  
The Common ◽  
Iterative Approximation Method ◽  
Fixed Point Sets

We introduce an iterative process for finding an element in the common fixed point sets of two continuous pseudocontractive mappings. As a consequence, we provide an approximation method for a common fixed point of a finite family of pseudocontractive mappings. Furthermore, our convergence theorem is applied to a convex minimization problem. Our theorems extend and unify most of the results that have been proved for this class of nonlinear mappings.

Sign in / Sign up

Export Citation Format

Share Document