Acta mathematica scientia, Series B >
VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS
Received date: 2014-10-20
Revised date: 2015-10-09
Online published: 2016-10-25
Supported by
The research was supported by National Natural Science Foundation of China (61503385) and Fundamental Research Funds for the Central Universities of China (3122016L002).
Let H1, H2, H3 be real Hilbert spaces, let A:H1→H3, B:H2→H3 be two bounded linear operators. The split equality common fixed point problem (SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi (Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis) is to find x∈F(U), y∈F(T) such that Ax=By, (1) where U:H1→H1 and T:H2→H2 are two nonlinear operators with nonempty fixed point sets F(U)={x∈H1:Ux=x} and F(T)={x∈H2:Tx=x}. Note that, by taking B=I and H2=H3 in (1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP (1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP (1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.
Jing ZHAO , Shengnan WANG . VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS[J]. Acta mathematica scientia, Series B, 2016 , 36(5) : 1474 -1486 . DOI: 10.1016/S0252-9602(16)30083-2
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