Iterative algorithm for the split equality problem in Hilbert spaces

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Godwin Chidi Ugwunnadi
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Equality Problem ◽  
Equality Problem

AbstractIn this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed algorithm to solution of the split equality problems (SEP).

scholarly journals An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Luoyi Shi ◽  
Ru Dong Chen ◽  
Yu Jing Wu
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Feasibility Problem ◽  
Linear Operators ◽  
Feasibility Problem ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Infinite Dimensional ◽  
Equality Problem ◽  
Split Feasibility

The multiple-sets split equality problem (MSSEP) requires finding a pointx∈∩i=1NCi,y∈∩j=1MQjsuch thatAx=By, whereNandMare positive integers,{C1,C2,…,CN}and{Q1,Q2,…,QM}are closed convex subsets of Hilbert spacesH1,H2, respectively, andA:H1→H3,B:H2→H3are two bounded linear operators. WhenN=M=1, the MSSEP is called the split equality problem (SEP). If  B=I, then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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.

scholarly journals Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Xu ◽  
Yuanheng Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Iterative Methods ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Infinite Family ◽  
Fixed Point Problems ◽  
Hierarchical Fixed Point ◽  
Hierarchical Fixed Point Problems

This paper deals with a new iterative algorithm for solving hierarchical fixed point problems of an infinite family of pseudocontractions in Hilbert spaces byyn=βnSxn+(1-βn)xn,xn+1=PC[αnf(xn)+(1-αn)∑i=1∞μi(n)Tiyn], and∀n≥0, whereTi:C↦His a nonselfki-strictly pseudocontraction. Under certain approximate conditions, the sequence{xn}converges strongly tox*∈⋂i=1∞F(Ti), which solves some variational inequality. The results here improve and extend some recent results.

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