A New Algorithm for Finding Fixed Points of Bregman Asymptotically Regular Quasi-Nonexpansive Mapping and Solutions of Equilibrium Problems

2021 ◽  
Author(s):  
R. Lotfikar ◽  
G. Zamani Eskandani
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Asymptotically Regular

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Yonghong Yao ◽  
Yeong-Cheng Liou
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Minimization Problem ◽  
Equilibrium Problems ◽  
Solution Set ◽  
Fixed Point Problems

The purpose of this paper is to solve the minimization problem of findingx∗such thatx∗=argminx∈Γ‖x‖2, whereΓstands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly tox∗.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

scholarly journals On Mann’s Method with Viscosity for Nonexpansive and Nonspreading Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nawab Hussain ◽  
Giuseppe Marino ◽  
Afrah A. N. Abdou
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Nonspreading Mapping ◽  
Type Mapping ◽  
Nonspreading Mappings

In the setting of Hilbert spaces, inspired by Iemoto and Takahashi (2009), we study a Mann’s method with viscosity to approximate strongly (common) fixed points of a nonexpansive mapping and a nonspreading mapping. A crucial tool in our results is the nonspreading-average type mapping.

Sign in / Sign up

Export Citation Format

Share Document