Hilbert空间中一类新的随机集值隐拟变分不等式

A new stochastic set-valued implicit quasi-variational inequalities in Hilbert spaces

随机集值隐拟变分不等式是变分不等式与不动点领域的一个重要分支,其被广泛的应用于博弈论、经济金融管理、物流管理等领域.研究了Hilbert空间中的一类新随机集值隐拟变分不等式问题。利用投影算子技巧、Nadler不动点定理以及不动点的随机化原理,给出了该类随机集值隐拟变分不等式解的存在性结果.所得结果,丰富了随机环境下随机变分不等式问题的可解性结果,包含的前人已有结果为特例.

This paper introduces and studies a new stochastic set-valued implicit quasi-variational inequality in a Hilbert space. By employing the technique of projection operator, the Nadler fixed point theorem and the randomization principle of fixed points, an existence of solutions was obtained for the new stochastic set-valued implicit quasi-variational inequality under mild conditions. The main result presented in this paper generalized some known results in the literature.