Auxiliary principle for completely generalized set-valued strongly nonlinear implicit variational inequalities. (English) Zbl 1229.47101
In this paper, a new class of variational inequalities, called completely generalized set-valued strongly nonlinear implicit variational inequality, is introduced. The iterative algorithm for this variational inequality with strongly monotone, relaxed Lipschitz and relaxed monotone mappings is established. Using the auxiliary principle technique, the existence of a solution for this class of variational inequalities is proven.
Reviewer: Zhang Xian (Xiamen)
MSC:
47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
47H04 | Set-valued operators |
47H05 | Monotone operators and generalizations |
47J25 | Iterative procedures involving nonlinear operators |
49J40 | Variational inequalities |