A minimax inequality in L-convex spaces and it application;

In this paper,utilizing the minimax inequality theorem in[1],we study the existence problem of solution for a new class of abstractly generalized bi-quasi-variational inequality.

A new minimax inequality theorem is established, which will be used to study the existence problem of solution for a new class of generalized bi-quasi-variational inequality.

Based on the property of convex and compactly closed set, the author generalizes Ky Fan minimax inequality as new minimax inequality of two functions on the product space of a topological vector space and a topological space, and from this obtains a minimax inequality about one function on this product space.

A section theorem, a minimax inequality and a generalized fixed point theorem where the underlying space is a product space of two topological vector spaces, are given.

By applying a minimax inequality and the auxiliary principle,some existence uniqueness theorems for solutions to the generalized strongly nonlinear variational inequalities are proved under the Setting of reflexive Banach spaces.

By using the invariance of the max-min inequality preperty of Jordan domain under quasiconformal mappings and the max-min inequality preperty of a disk,the papar proves that the quasidisk has the max-min inequality property too.

By applying existence theorems of maximal elements for a family of GB _majorized mappings in a product space of G _convex spaces,some coincidence theorem,Fan_Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G _convex spaces.