Banach空间中含$(\emph{\textbf{H}},\bm\phi)$-$\bm\eta$-单调算子的变分包含组

在实的一致光滑Banach空间中, 引入一类新的含$(H,\phi)$-$\eta$-单调算子的变分包含组. 利用$(H,\phi)$-$\eta$-单调算子的近似映射技巧, 证明了此类新的变分包含组解的存在性与唯一性, 并构造了逼近此类变分包含组解 的迭代算法; 讨论了由此迭代算法生成的迭代序列的收敛性. 所得结果推广与改进了文献中的一些主要结果.

System of variational inclusions with (H, φ)-η-monotone operators in Banach spaces

This paper introduced a new system of variational inclusions with(H,Φ)-η-monotone operators in real uniformly smooth Banach spaces.By using the proximal mapping technique associated with(H,Φ)-η-monotone operators,we proved the existence and uniqueness of solution for this new system and construct a new iterative algorithm for approximating the solution of this system.The convergence of the iterative sequence generated by the iterative algorithm was also discussed.The results extend and improve some known results in the literature.