对带误差项的Banach空间中完全广义集值拟变分包含的摄动迭代算法(英文)

Perturbed Iterative Algorithms for Completely Generalized Set-Valued Quasi Variational Inclusions in Banach Spaces with Errors

研究了一类新的实Banach空间中的广义集值拟变分包含:f ∈ N(x,y)+M(z,v)+W(g(u)-h(w),u),它包含了近几年许多作者所作的变分包含问题.在实Banach空间中,利用极大增生算子的性质,建立了Banach空间中的广义集值拟变分包含和不动点问题间的等价性.利用这种等价性,建立了一些摄动迭代算法,并证明了近似解序列强收敛于精确解.本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果.

In this paper, a new class of generalized set-valued quasi variational inclusions in Banach spaces are studied, which include many variational inclusions studied by others in recent years. Using the resolvent operator technique, we establish the equivalence between the generalized set-valued quasi variational inclusions in Banach spaces and the fixed point problems, and some perturbed iterative algorithms, prove that its proximate solution converges to its exact solution in real Banach spaces. Our results improve and generalize many known corresponding algorithms and results.