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A Self-Adaptive Algorithm for Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings
Acta Applicandae Mathematicae ( IF 1.6 ) Pub Date : 2020-10-07 , DOI: 10.1007/s10440-020-00362-6
Suthep Suantai , Pachara Jailoka

In this work, we study the split null point problem and the fixed point problem in Hilbert spaces. We introduce a self-adaptive algorithm based on the viscosity approximation method without prior knowledge of the operator norm for finding a common solution of the considered problem for maximal monotone mappings and demicontractive multivalued mappings. A strong convergence result of our proposed algorithm is established under some suitable conditions. Some convergence results for the split feasibility problem and the split minimization problem are consequences of our main result. Finally, we also give numerical examples for supporting our main result.



中文翻译:

减半多值映象的分裂零点问题和不动点问题的自适应算法

在这项工作中,我们研究希尔伯特空间中的分裂零点问题和不动点问题。我们引入了一种基于粘度近似方法的自适应算法,无需事先了解算子范数,即可找到最大单调映射和非收缩多值映射所考虑问题的通用解。在某些合适的条件下,我们提出的算法具有很强的收敛性。分裂可行性问题和分裂最小化问题的一些收敛性结果是我们主要结果的结果。最后,我们还提供了数值示例来支持我们的主要结果。

更新日期:2020-10-07
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