一类具有Lipschitz条件的非线性变分包含问题解的存在性和Ishikawa迭代逼近问题

Existence and Ishikawa Iterative Approximation Problem of Solutions for Certain Nonlinear Variational Inclusions with Lipschitz Condition

研究实自反Banach空间中一类具有Lipschitz条件的强增生型变分包含问题g(u)∈D(ηφ)〈Tu-Au-f,η(υ,g(u))〉≥φ(g(u))-φ(υ)υ∈X*得到了其解的存在性、唯一性及其具有混合误差项的Ishikawa迭代程序的收敛性的一些相关结果.

The purpose of this paper is to study a class of variational inclusions problem with Lipschitz condition and strongly accretive type mappings in real reflexive Banach spaces. {g（u）∈D（ ηφ） 〈Tu-Au-f, η（v,g（u））〉≥φ（g（u））-φ（v） A↓v∈X It is obtained that some corresponding results for existence and uniqueness of solutions to this class of variational inclusions and the convergence of Ishikawa iteration process.