In this paper, the concept of two point probability contractor is introduced in Nonarachimedean PN space, some existence theorems and uniqueness theorems for the solution of nonlinear operator equations are obtained, the results are generalization of results of [4].

In this paper, the concept of two point probability contractor is introduced in PN space,it is probabitized for the concept of two point contractor,so some existence and uniqueness the orems for the solution of nonlinear operator equations in PN space are obtained,this results are generaliization of results of some authors.

The purpose of this paper is to introduce the concept of (Φ,Δ)-type probabi listic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with the probabilistic contractor in Menger PN-spaces.

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.

Three important reference functions including porosity,two-point probability function and linear path function for constructing digital core are listed.

The purpose of this paper is to introduce the concept of probabilistic directed contractor,and by transfinite induction it has also studied the global and locally existence problems of solutions for set-valued nonlinear operator equations with probabilistic directed contractor and the existence of fixed points for set-valued mappings.