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 A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 226 ◽  
Author(s):  
Wachirapong Jirakitpuwapat ◽  
Poom Kumam ◽  
Yeol Cho ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Signal Processing ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Operator Norm ◽  
Point Problem ◽  
Convergence Theorems ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

In 2014, Cui and Wang constructed an algorithm for demicontractive operators and proved some weak convergence theorems of their proposed algorithm to show the existence of solutions for the split common fixed point problem without using the operator norm. By Cui and Wang’s motivation, in 2015, Boikanyo constructed also a new algorithm for demicontractive operators and obtained some strong convergence theorems for this problem without using the operator norm. In this paper, we consider a viscosity iterative algorithm in Boikanyo’s algorithm to approximate to a solution of this problem and prove some strong convergence theorems of our proposed algorithm to a solution of this problem. Finally, we apply our main results to some applications, signal processing and others and compare our algorithm with five algorithms such as Cui and Wang’s algorithm, Boikanyo’s algorithm, forward-backward splitting algorithm and the fast iterative shrinkage-thresholding algorithm (FISTA).

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 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 The split common fixed point problem of two infinite families of demicontractive mappings and the split common null point problem

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3859-3874 ◽  
Author(s):  
Ali Abkar ◽  
Elahe Shahrosvand
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Problem ◽  
Null Point ◽  
Inclusion Problem ◽  
Point Problem ◽  
Variational Inclusion Problem ◽  
Common Fixed Point Problem ◽  
Demicontractive Mappings ◽  
Split Common Fixed Point

In this paper we introduce a new algorithm based on the viscosity iteration method for solving the split common fixed point problem of two infinite families of k-demicontractive mappings. We shall also study the split common null point problem, and the split equilibrium problem for this class of mappings. As an application, we obtain strong convergence theorems for the split monotone variational inclusion problem and the split variational inequality problem. Our results improve and extend the recent results of Cui and Wang [9], Takahashi [21], Tang and Lui [22], Moudafi [15], Eslamian and Vahidi [17], and many others.

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