Weak and strong convergence theorems for asymptotically pseudo-contraction mappings in the intermediate sense in Hilbert spaces

2012 ◽  
Vol 56 (1) ◽  
pp. 165-183 ◽  
Author(s):  
Lai-Jiu Lin ◽  
Zenn-Tsun Yu ◽  
Chih-Sheng Chuang
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Contraction Mappings

scholarly journals Inertial Extragradient Methods for Solving Split Equilibrium Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1884
Author(s):  
Suthep Suantai ◽  
Narin Petrot ◽  
Manatchanok Khonchaliew
Keyword(s):  
Strong Convergence ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Equilibrium Problems ◽  
Constraint Qualifications ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Extragradient Methods

This paper presents two inertial extragradient algorithms for finding a solution of split pseudomonotone equilibrium problems in the setting of real Hilbert spaces. The weak and strong convergence theorems of the introduced algorithms are presented under some constraint qualifications of the scalar sequences. The discussions on the numerical experiments are also provided to demonstrate the effectiveness of the proposed algorithms.

scholarly journals Multiple-Set Split Feasibility Problems forκ-Strictly Pseudononspreading Mapping in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Jing Quan ◽  
Shih-sen Chang ◽  
Xiang Zhang
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Weak And Strong Convergence ◽  
Convergence Theorems ◽  
Infinite Dimensional ◽  
Split Feasibility Problems ◽  
Split Feasibility ◽  
Strictly Pseudononspreading Mapping

The purpose of this paper is to prove some weak and strong convergence theorems for solving the multiple-set split feasibility problems forκ-strictly pseudononspreading mapping in infinite-dimensional Hilbert spaces by using the proposed iterative method. The main results presented in this paper extend and improve the corresponding results of Xu et al. (2006), of Osilike et al. (2011), and of many other authors.

scholarly journals Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 167 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Suparat Kesornprom ◽  
Nattawut Pholasa
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Inclusion Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Convergence Theorems

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.

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