scholarly journals Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1307
Author(s):  
Lili Chen ◽  
Ni Yang ◽  
Jing Zhou
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Strong Convergence ◽  
Approximation Method ◽  
Variational Inequality Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Banach Limits ◽  
Weak Convergence Theorem ◽  
The Common

In this paper, we first propose the concepts of (ζ,η,λ,π)-generalized hybrid multi-valued mappings, the set of all the common attractive points (CAf,g) and the set of all the common strongly attractive points (CsAf,g), respectively for the multi-valued mappings f and g in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets Af, Ff and CAf,g for the multi-valued mappings f and g in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two (ζ,η,λ,π)-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.

scholarly journals Viscosity approximation method for solving variational inequality problem in real Banach spaces

2021 ◽  
pp. 1-20
Author(s):  
Godwin Ugwunnadi
Keyword(s):  
Variational Inequality ◽  
Banach Spaces ◽  
Approximation Method ◽  
Variational Inequality Problem ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Inequality Problem ◽  
Mild Conditions ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.

scholarly journals Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

2019 ◽  
Vol 52 (1) ◽  
pp. 347-360
Author(s):  
Mujahid Abbas ◽  
Hira Iqbal ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Approximation Method ◽  
Multivalued Mappings ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Multivalued Nonexpansive Mapping ◽  
Convergence Results

AbstractWe prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.

scholarly journals Strong convergence for nonexpansive mappings by viscosity approximation methods in Hadamard manifolds

2015 ◽  
Vol 4 (2) ◽  
pp. 299
Author(s):  
Mandeep Kumari ◽  
Renu Chugh
Keyword(s):  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Approximation Method ◽  
Nonexpansive Mappings ◽  
Approximation Methods ◽  
Hadamard Manifolds ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Viscosity Approximation Methods

<p>In 2010, Victoria Martin Marquez studied a nonexpansive mapping in Hadamard manifolds using Viscosity approximation method. Our goal in this paper is to study the strong convergence of the Viscosity approximation method in Hadamard manifolds. Our results improve and extend the recent research in the framework of Hadamard manifolds.</p>

scholarly journals Viscosity Approximation Methods for Nonexpansive Multi-Valued Nonself Mappings and Equilibrium Problems

2014 ◽  
Vol 47 (2) ◽  
Author(s):  
P. Cholamjiak ◽  
W. Cholamjiak ◽  
S. Suantai
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Approximation Method ◽  
Equilibrium Problems ◽  
Approximation Methods ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Convergence Theorems ◽  
Viscosity Approximation Methods

AbstractIn this paper, strong convergence theorems by the viscosity approximation method for nonexpansive multi-valued nonself mappings and equilibrium problems are established under some suitable conditions in a Hilbert space. The obtained results extend and improve the corresponding results existed in the literature.

An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Adrian Petruşel ◽  
Jen-Chih Yao
Keyword(s):  
Variational Inequality ◽  
Iterative Process ◽  
Variational Inequality Problem ◽  
Iterative Scheme ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Viscosity Approximation ◽  
Inverse Strongly Monotone ◽  
The Common ◽  
Viscosity Approximation Methods

AbstractIn this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.

scholarly journals The Conjugate Gradient Viscosity Approximation Algorithm for Split Generalized Equilibrium and Variational Inequality Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Meixia Li ◽  
Haitao Che ◽  
Jingjing Tan
Keyword(s):  
Variational Inequality ◽  
Approximation Algorithm ◽  
Conjugate Gradient ◽  
Variational Inequality Problem ◽  
Viscosity Approximation ◽  
Common Solution ◽  
Mild Conditions ◽  
Generalized Equilibrium ◽  
The Common ◽  
Split Generalized Equilibrium Problem

In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. The conclusion presented in this paper is the generalization, extension, and supplement of the previously known results in the corresponding references. Some numerical results are illustrated to show the feasibility and efficiency of the proposed algorithm.

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