L_p空间中Lipschitz强单调算子方程解的迭代算法
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摘要
设E=L_p(1强单调算子.给出了L_p空间中Lipschitz强单调算子方程解的迭代构造算法,并证明由此算法构造的序列强收敛于A_x=0的唯一解,所得结果改进和推广了已有文献的相关结果.
Let E=L_p(1
Let E=L_p(1
引文
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[7]CHIDUME C E,BELLO A U,USMAN B.Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces[J].Springer Plus,2015,4(1):1-9.
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[9]ALBER Y I.Metric and Generalized Projection Operators in Banach Spaces:Properties and Applications in Theory and Applications of Nonlinear Operators of Monotone and Accretive Type[M].New York:Springer,1996.
[2]BRUCK R E.A strongly convergent iterative solution of 0∈U(x)for a maximal monotone operator U in Hilbert space[J].Journal of Mathematical Analysis and Applications,1974,48(1):114-126.
[3]NEVANLINNA O.Global iteration schemes for monotone operators[J].Nonlinear Analysis,1979,3(4):505-514.
[4]ROCKAFELLAR R T.Monotone operators and the proximal point algorithm[J].Siam Journal Control and Optimization,1976,14(5):877-898.
[5]游兆永,刘昆昆.无界集上Lipschitz单调映射方程的迭代解法[J].西安交通大学学报,1989,23(1):19-25.YOU Z Y,LIU K K.Iterative solution for equations of Lipschitzian monotonic mappings on unbounded set[J].Journal of Xi’an Jiaotong University,1989,23(1):19-25.
[6]徐宗本.关于单调算子方程构造可解性问题的解答[J].自然杂志,1984,7(8):633.XU Z B.Solutions to the construction of solvability problems for monotone operator equations[J].Chinese Journal of Nature,1984,7(8):633.
[7]CHIDUME C E,BELLO A U,USMAN B.Krasnoselskii-type algorithm for zeros of strongly monotone Lipschitz maps in classical Banach spaces[J].Springer Plus,2015,4(1):1-9.
[8]KAMIMURA S,TAKAHASHI W.Approximating solutions of maximal monotone operators in Hilbert space[J].Journal of Approximation Theory,2000,106(2):226-240.
[9]ALBER Y I.Metric and Generalized Projection Operators in Banach Spaces:Properties and Applications in Theory and Applications of Nonlinear Operators of Monotone and Accretive Type[M].New York:Springer,1996.