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VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS 被引量:1
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作者 赵静 王盛楠 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1474-1486,共13页
Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudaf... Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;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 : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H;: Ux = x} and F(T) = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;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. 展开更多
关键词 split equality common fixed point problems quasi-nonexpansive operator strong convergence viscosity iterative algorithms Hilbert space
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STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES 被引量:1
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作者 张石生 王林 +1 位作者 秦丽娟 马招丽 《Acta Mathematica Scientia》 SCIE CSCD 2016年第6期1641-1650,共10页
The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Und... The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility prob- lems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new. 展开更多
关键词 the split equality variational inclusion problem in Banach space split feasibilityproblem in Banach space split equilibrium problem in Banach spaces
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