Φ-强单调半连续映象的Browder变分不等式解的Ishikawa迭代算法

The Ishikawa Iterative Algorithms to Solutions of Browder Variational Inequalities with Φ-Strongly Monotone and Semicontinuous Mapping

在H ilbert空间H中,在T∶H→H有界,Φ-强单调和半连续条件下,利用次微分φ算子的性质,将求变分不等式〈Tu-f,y-u〉≥φ(u)-φ(y),y∈X的解转化成求集值Φ-强伪压缩映象的不动点,得到B rowder变分不等式〈Tu-f,y-u〉≥φ(u)-φ(y),y∈H的带有误差的Ish ikawa迭代算法,在适当假设下证明了该迭代算法强收敛于不等式的唯一解。本文结果改进和推广了文献中部分已知的结果。

In Hilbert space H, we obtain the Ishikawa iterative algorithms with errors to solutions of Browder variational inequalities （Tu-f,y- u）≥φ（u）-φ（Y）, arbitary y ∈ H with Ф-Strongly Monotone,bounded and Semi-continuous Mapping T：H→ H. The results of this paper improve and generalize many known results in the literature.