scholarly journals Strong Convergence Theorems for an Implicit Iterative Algorithm for the Split Common Fixed Point Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Huimin He ◽  
Sanyang Liu ◽  
Rudong Chen
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
All Solutions ◽  
Split Common Fixed Point ◽  
Implicit Iterative Algorithm

The aim of this paper is to construct a novel implicit iterative algorithm for the split common fixed point problem for the demicontractive operatorsU,T, and  xn=αnfxn+1-αnUλxn-ρnA*I-TAxn,n≥0, whereUλ=(1-λ)I+λU, and we obtain the sequence which strongly converges to a solutionx^of this problem, and the solutionx^satisfies the variational inequality.〈x^-f(x^),x^-z〉≤0,∀z∈S, whereSdenotes the set of all solutions of the split common fixed point problem.

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 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.

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