Banach空间中变分包含组问题的强收敛性

A Strong Convergence Theorem for a General System of Variational Inclusions in Banach Spaces

本文主要介绍了Banach空间中的变分包含组问题,同时构造了用于就解决逆强增生映像的变分包含组问题和λ-强伪压缩映射的公共不动点问题解的迭代方法。在一定的条件下,当空间为一致凸且q-一致光滑的Banach空间时,结合经典的向前向后分裂方法,完成了问题解的强收敛性的证明。

In this paper, a general system of variational inclusion in Banach spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly ac-cretive mapping and common set of fixed points for a λ-strict pseudocontraction is established. Under the suitable conditions, by forward-backward splitting method, it is proved that there is strong convergence theorem for the problem in uniformly convex and q-uniformly smooth Banach spaces.