(q^-)一致光滑Banach空间中含(H,η)-增生算子的一类非线性集值变分包含组的迭代算法问题

Iterative Algorithm Problems on System of Nonlinear Set-Valued Variational Inclusions with (H,η)-Accretive Operator in q Uniformly Smooth Banach Space

引入(H,η)-增生这一类广义增生算子,通过研究这类(H,η)-增生算子的性质,把m-增生算子预解算子的概念扩展到(H,η)-增生算子.利用这一新的预解算子技巧,在Banach空间中证明了一类新的变分包含组的解的存在性和唯一性,同时也建立了一类新的算法来逼近这一变分包含组的解,并讨论了这一算法产生的迭代序列的收敛性.

We introduced a new class of generalized accretive operators named （H, η）- accretive,and by studying the properties of （H, η） - accretive operator, we extended the concept of resolvent operators associated with accretive operator to the new （H, η）- accretive operators. By the new resolvent operator technique, we proved the existence and uniqueness of solutions for this new system of variational inclusions in Banach space, meanwhile, we also established a new algorithm for approximating the solution of this system and discussed the convergence of the sequence of iterates generated by the algorithm.