scholarly journals Fixed point theorems for a class of nonlinear operators in Hilbert spaces with lattice structure and application

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yujun Cui ◽  
Jingxian Sun
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Lattice Structure ◽  
Nonlinear Operators

scholarly journals FIXED POINT THEOREMS FOR NEW GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES AND APPLICATIONS

2013 ◽  
Vol 17 (5) ◽  
pp. 1597-1611 ◽  
Author(s):  
Wataru Takahashi ◽  
Ngai-Ching Wong ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theorems

scholarly journals Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Eskandar Naraghirad ◽  
Ngai-Ching Wong ◽  
Jen-Chih Yao
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Weak And Strong Convergence ◽  
Bregman Distances ◽  
Opial Property ◽  
Nonspreading Mappings

The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.

scholarly journals Fixed point theorems for compact potential operators in Hilbert spaces

2017 ◽  
Vol 18 (2) ◽  
pp. 493-502
Author(s):  
A. Boucenna ◽  
◽  
S. Djebali ◽  
T. Moussaoui ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Potential Operators

scholarly journals New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with applications in Hilbert spaces

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1677-1693 ◽  
Author(s):  
Shenghua Wang ◽  
Yifan Zhang ◽  
Ping Ping ◽  
Yeol Cho ◽  
Haichao Guo
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Convex Combination ◽  
Projection Methods ◽  
Extragradient Methods ◽  
Numerical Examples

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

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