Banach空间中的广义H-η-增生算子及其在变分包含中的应用

Generalized H-η-Accretive Operators in Banach Spaces With an Application to Variational Inclusions

在Banach空间中,引入和研究了新的广义H-η-增生算子,对广义m-增生算子与H-η-单调算子提供了一个统一的框架.还定义了广义H-η-增生算子相应的预解算子,并且证明了其Lipschitz连续性.作为应用,考虑了涉及广义H-η-增生算子的一类变分包含问题的可解性.利用预解算子方法,构造了一个求解变分包含的迭代算法.在适当假设下,证明了变分包含解的存在性和由算法生成的迭代序列的收敛性.

A new notion of generalized H-y-accretive operator which provided a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces was introduced and studied. A resolvent operator associated with the generalized H-η-accretive operator was defined and its Lipschitz continuity was shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces was considered. By using the technique of resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach space was constructed. Under some suitable conditions, the existence of solution for the variational inclusion and the convergence of iterative sequence generated by the algorithm were proved.