Strong and Weak Convergence Theorems for General Mixed Equilibrium, General Variational Inequality, and Fixed Point Problems for Two Nonexpansive Semigroups in Hilbert Spaces

2021 ◽  
Author(s):  
Baoshuai Zhang ◽  
Ying Tian
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Nonexpansive Semigroups ◽  
General Variational Inequality ◽  
Mixed Equilibrium

Strong and weak convergence theorems for general mixed equilibrium problems and general variational inequality problems and fixed point problems for two nonexpansive semigroups in Hilbert spaces

2021 ◽  
pp. 152-160
Author(s):  
Baoshuai Zhang ◽  
◽  
Ying Tian ◽  
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Common Element ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Nonexpansive Semigroups ◽  
General Variational Inequality ◽  
Mixed Equilibrium

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and the set of solutions of a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results announced by many others.

scholarly journals Extragradient algorithms for variational inequality, fixed point and generalized mixed equilibrium problems

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1021-1030
Author(s):  
Baohua Guo ◽  
Lijuan Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is to investigate variational inequalities, fixed point problems and generalized mixed equilibrium problems. Anextragradient iterative algorithm is investigated in the framework of Hilbert spaces. Weak convergence theorems for common solutions are established.

scholarly journals Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 922
Author(s):  
Marwan A. Kutbi ◽  
Abdul Latif ◽  
Xiaolong Qin
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Monotone Mappings ◽  
Projection Algorithms ◽  
Convergence Theorems ◽  
Expansive Mapping ◽  
Computational Errors ◽  
Zero Points

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

The strong convergence theorems for the split equality fixed point problems in Hilbert spaces

2018 ◽  
Vol 12 (6) ◽  
pp. 255-270
Author(s):  
Jun Niu ◽  
Zheng Zhou ◽  
Jian-Qiang Zhang ◽  
Li-Juan Qin
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Convergence Theorems

Strong and weak convergence theorems for fixed points of a class of nonlinear mappings

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Changqun Wu ◽  
Zhiqiang Wei ◽  
Yu Li
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Weak Convergence Theorem

AbstractIn this paper, the class of total asymptotically nonexpansive mappings is considered. A weak convergence theorem of Mann-type iterative algorithm is established. Hybrid projection methods are considered for the class of total asymptotically nonexpansive mappings. Strong convergence theorems are also established in the framework of Hilbert spaces.

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