关于( H,η)单调算子的非线性集值算子包含的迭代算法(英文)

An Iterative Algorithm for Nonlinear Set-Valued Operator Inclusions Involving (H, η)-Monotone Operators

引进了关于H和G的强单调性概念,在Hilbert空间中研究了新的一类关于( H,η)单调算子的非线性集值算子包含.应用与( H,η)单调算子相关的预解算子技巧提出了一个迭代算法逼近其解,并且讨论了由此算法产生的迭代序列的收敛特征.

The concept of strongly monotonicity with respect to H and G and a new kind of nonlinear set-valued operator inclusions （NSVOI） with （H, η）-monotone operators are introduced in Hilbert space. Using resolvent operator technique associated with an （H, η）-monotone operator, the authors suggest a new iterative algorithm for approximating a solution to （NSVOI） and also discuss the convergence criteria of iterative sequences generated by the algo- rithm.