The purpose of this paper is to introduce the coucept of probabilistic contractor couple in Menger probabilistic normed spaces and to study the existence and uniqueness of solutions for a system of nonlinear operator equations with probabilistci contractor couples in Menger probabilistic normed spaces.

S-convex and K-convex in a probabilistic normed space;

This paper proves that every probabilistic contraction map from E to E has a unique fixed point, where E is a complete and uniformly local semi-convex probabilistic normed space, and obtains a fixed point theorem in metric linear spaces.

This dissertation deals with some new fixed point theorems in Menger probabilistic metric spaces, which include common fixed point theorems of weakly compatible mappings under strict contractive conditions and common fixed point theorems of compatible and weakly compatible mappings underφ-contractive conditions.

A kind of set-valued differential(γ-subdifferential) of functionals in normed linear space was defined,and its properties and application to nonsmooth multiobjective programming problem was discussed,so that some new results were obtained.

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.