A New Class of Generalized Nonlinear Variational Inequalities Problem in Hilbert Space
LUO Jing;LONG Jianjun;School of Science,Sichuan University of Science & Engineering;Dahe Middle School of Panzhihua;
Variational inequality principle is a powerful research tool in the current mathematical technology,and has important academic research value and significance. It is widely and importantly applied in operations research,computer science,system science,engineering technology,transportation,economic and management and other aspects. In this essay,by using the resolvent operator technique and the auxiliary principle technique of η a differential operator,a class of generalized nonlinear variational inequalities problem in Hilbert space is researched,and the solution of the problem is obtained. On this basis,a auxiliary problem with Lipschitz continuous,strongly monotone and relaxed monotone mapping is introduced,and the existence and the uniqueness of the solution are proved by using the resolvent operator and the fixed point theorem of set-valued contractive mappings. This result has extended,improved and developed the results in relevant literatures.