带误差项的广义集值变分包含

Generaliced Set-valued Variational Inclusion with Error Term

研究了一类新的广义集值变分包含 :0∈N(w ,y) +A(z,u) .在实Hilbert空间中 ,利用极大单调算子的性质 ,建立了广义集值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 .

This paper studied a new generalized set-valued variational inclusions : 0∈N(w,y)+A(z,u),which included many variational inclusions studied by others in recent years. Using the resolvent technique, we established the equivalence between the generalized set-valued variational inclusions and the fixed point problems, and some perturbed iterative algorithms, proved that its proximate solution converge to its exact solution in real Hilbert space. Our results improve and generalized many known corresponding algorithms and results.