scholarly journals Strong Convergence Theorems for the Split Common Fixed Point Problem for Countable Family of Nonexpansive Operators

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Cuijie Zhang ◽  
Songnian He
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Countable Family ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
Split Common Fixed Point

We introduce a new iterative algorithm for solving the split common fixed point problem for countable family of nonexpansive operators. Under suitable assumptions, we prove that the iterative algorithm strongly converges to a solution of the problem.

scholarly journals Strong Convergence Theorems for the Generalized Split Common Fixed Point Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Cuijie Zhang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Convergence Theorems ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
The Common ◽  
Split Common Fixed Point

We introduce the generalized split common fixed point problem (GSCFPP) and show that the GSCFPP for nonexpansive operators is equivalent to the common fixed point problem. Moreover, we introduce a new iterative algorithm for finding a solution of the GSCFPP and obtain some strong convergence theorems under suitable assumptions.

scholarly journals Weak and Strong Convergence of an Algorithm for the Split Common Fixed-Point of Asymptotically Quasi-Nonexpansive Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazheng Dang ◽  
Yan Gao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Weak And Strong Convergence ◽  
Convergence Results ◽  
Common Fixed Point Problem ◽  
Nonexpansive Operators ◽  
Split Common Fixed Point

Inspired by the Moudafi (2010), we propose an algorithm for solving the split common fixed-point problem for a wide class of asymptotically quasi-nonexpansive operators and the weak and strong convergence of the algorithm are shown under some suitable conditions in Hilbert spaces. The algorithm and its convergence results improve and develop previous results for split feasibility problems.

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

scholarly journals Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

2019 ◽  
pp. 35-50
Author(s):  
Yusuf Ibrahim
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Asymptotically Nonexpansive ◽  
Split Common Fixed Point

In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition

Solving split equality common fixed point problem for infinite families of demicontractive mappings

2018 ◽  
Vol 34 (3) ◽  
pp. 321-331
Author(s):  
ADISAK HANJING ◽  
◽  
SUTHEP SUANTAI ◽  
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings

In this paper, we consider the split equality common fixed point problem of infinite families of demicontractive mappings in Hilbert spaces. We introduce a simultaneous iterative algorithm for solving the split equality common fixed point problem of infinite families of demicontractive mappings and prove a strong convergence of the proposed algorithm under some control conditions.

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