A Generalized Proximal Point Algorithm and Implicit Iterative Schemes for a Sequence of Operators on Banach Spaces

2007 ◽  
Vol 16 (5-6) ◽  
pp. 597-619 ◽  
Author(s):  
Yasunori Kimura ◽  
Wataru Takahashi
Keyword(s):  
Banach Spaces ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Iterative Schemes ◽  
Generalized Proximal Point Algorithm

scholarly journals Iterative methods for solving split feasibility problems and fixed point problems in Banach spaces

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5345-5353
Author(s):  
Min Liu ◽  
Shih-Sen Changb ◽  
Ping Zuo ◽  
Xiaorong Li
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Recent Result ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Split Feasibility Problems ◽  
Split Feasibility

In this paper, we consider a class of split feasibility problems in Banach space. By using shrinking projective method and the modified proximal point algorithm, we propose an iterative algorithm. Under suitable conditions some strong convergence theorems are proved. Our results extend a recent result of Takahashi-Xu-Yao (Set-Valued Var. Anal. 23, 205-221 (2015)) from Hilbert spaces to Banach spaces. Moreover, the method of proof is also different.

Generalized super-relaxed proximal point algorithms involving relative A-maximal relaxed accretive in Banach spaces

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Mohsen Alimohammady ◽  
Morteza K. Kalleji
Keyword(s):  
Banach Spaces ◽  
General Framework ◽  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Proximal Point Algorithms

Abstract.A general framework for a relaxed proximal point algorithm using the notion of

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