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Solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators

JOURNAL OF INEQUALITIES AND APPLICATIONS 2018年第1期2018卷 83-83页

作者： Zhao, Jing Zong, Haili Civil Aviat Univ China Tianjin Key Lab Adv Signal Proc Tianjin Peoples R China Civil Aviat Univ China Coll Sci Tianjin Peoples R China

In this paper, we propose parallel and cyclic iterative algorithms for solving the multiple-set split equality common fixed-point problem of firmly quasi-nonexpansive operators. We also combine the process of cyclic and parallel iterative methods and propose two mixed iterative algorithms. Our several algorithms do not need any prior information about the operator norms. Under mild assumptions, we prove weak convergence of the proposed iterative sequences in Hilbert spaces. As applications, we obtain several iterative algorithms to solve the multiple-set split equality problem.

关键词： the multiple-set split equality common fixed-point problem The multiple-set split equality problem Firmly quasi-nonexpansive mapping Weak convergence Iterative algorithms Hilbert space

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Mixed iterative algorithms for the multiple-set split equality common fixed-point problems without prior knowledge of operator norms

引用

OPTIMIZATION 2016年第5期65卷 1069-1083页

作者： Zhao, Jing Wang, Shengnan Civil Aviat Univ China Dept Math Tianjin Peoples R China

Let H-1, H-2, H-3 be real Hilbert spaces, let A : H-1 -> H-3, B : H-2 -> H-3 be two bounded linear operators. the multiple-set split equality common fixed-point problem (MSECFP) under consideration in this paper is to find x is an element of boolean AND(p)(i=1) F(U-i), y is an element of boolean AND(r)(j=1) F(T-j) such that Ax = By, (0.1) where p, r >= 1 are integers, U-i : H-1 -> H-1 (1 <= i <= p) and Tj : H-2 -> H-2 (1 <= j <= r) are quasi-nonexpansive mappings with nonempty fixed-point sets. Note that, the above problem (1) allows asymmetric and partial relations between the variables x and y. If B = I and H-2 = H-3, then the MSECFP (1) reduces to the multiple-set split common fixed-point problem proposed by Censor et al. In this paper, we introduce mixed cyclic and simultaneous iterative algorithms for the MSECFP (1). We introduce a way of selecting the stepsizes such that the implementation of our algorithms does not need any prior information about the operator norms. Weak convergence results are given.

关键词： the multiple-set split equality common fixed-point problem quasi-nonexpansive mapping weak convergence iterative algorithms Hilbert space

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