scholarly journals Strong Convergence of Iterative Schemes for Zeros of Accretive Operators in Reflexive Banach Spaces

2010 ◽  
Vol 2010 (1) ◽  
pp. 103465 ◽  
Author(s):  
JongSoo Jung
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Accretive Operators ◽  
Reflexive Banach Spaces ◽  
Iterative Schemes

Strong convergence of composite iterative schemes for zeros of m-accretive operators in Banach spaces

2009 ◽  
Vol 70 (5) ◽  
pp. 1830-1840 ◽  
Author(s):  
L.-C. Ceng ◽  
A.R. Khan ◽  
Q.H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Accretive Operators ◽  
Iterative Schemes

scholarly journals Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 156 ◽  
Author(s):  
Chanjuan Pan ◽  
Yuanheng Wang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Splitting Method ◽  
Splitting Methods ◽  
Strong Convergence Theorem ◽  
Accretive Operators ◽  
Convex Minimization Problem ◽  
Inertial Extrapolation

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

scholarly journals Strong Convergence Theorems for Quasi-Bregman Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mohammed Ali Alghamdi ◽  
Naseer Shahzad ◽  
Habtu Zegeye
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Finite Family ◽  
Monotone Mappings ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

We study a strong convergence for a common fixed point of a finite family of quasi-Bregman nonexpansive mappings in the framework of real reflexive Banach spaces. As a consequence, convergence for a common fixed point of a finite family of Bergman relatively nonexpansive mappings is discussed. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common solution of a finite family equilibrium problem and a common zero of a finite family of maximal monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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