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 paper studies fixed points theorems about contraction mapping on probabilistic normed space.

The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

We also introduce some fixed point Theorems for contraction mappings and common fixed point theorems For set-valued mappings in topological spaces with topological Distances family.

Let C be a closed convex subset of E,f:C→C be a contractive mapping,and T:C→C be a nonexpansive mapping.

A general Kannan contractive mapping is introduced and a fixed point theorem is given, meanwhile,some important results of the paper are improved and developed.

This paper introduces class of more general contractive mappings in Fuzzy metric space introduced by Kramosil and Michalek.

Three contraction properties (probabilistic contraction, random contraction, metric contraction),random Ekeland variational principleand randomCaristi fixed pointtheorem,and the relationships between them and completeness are discussed in random metric space.

The existence of common fixed points of generalized contractive mapping pairs was also discussed.

If φ strongly accretive mapping or φ strongly pseudocontractive mapping on real Banach space are lower semi continuous, then they are single valued.