Menger PN-spaces Research Articles

1-set-contractive perturbations of accretive operators in Menger PN-spaces

Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.

Applications of the fixed point index in Menger PN-spaces

In this paper, applications of the fixed-point index of a nonlinear operator in Menger PN-spaces are given. Theorems on the existence of fixed points of a compact continuous operator are obtained. At the same time, the existence of the solution of a class of differential equations in a complete Menger PN-space is studied, and the theorem on the existence of the solution of a class of differential equations is obtained.

Some Nonlinear Problems in M-PN Spaces

Some new bounded conditions are constructed in Menger PN spaces,meanwhile,solutions of some nonlinear operator equations are obtained by virtue of topological degree.The main results obtained in this paper improve the recent ones.Furthermore,the new conclusions are applied to a special equation.

The fixed-point index of nonlinear operators in Menger PN-spaces

In the paper, the topological degree for a compact continuous operator defined on an open subset of a Menger PN-space is generalized. The new concept of fixed-point index in Menger PN-spaces is introduced, themost important properties of the fixed-point index are established, and some other results are given.

Strong Probabilistic Contractor Couple and Nonlinear Operator Equations in Menger PN Space

The purpose of the paper is to introduce the concept of strong probabilistic contractor couple in Menger PN spaces and to study the existence and uniqueness of solutions for a system of nonlinear operator equations with probabilistic contractor couples in Menger PN spaces non-Archimedean Menger PN spaces.

Research on some problems for nonlinear operators

In this paper, we discuss some problems for nonlinear operators in the Menger PN space. Meanwhile, we prove existence theorems for the solution of an operator equation, and obtain some new results by means of the theory of topological degree for the Z-P-S space.

The topological degree of A-proper mapping in the Menger PN-space (II)

In the paper “The topological degree of A-proper mapping in the Menger PN-space (I)”, the new concept of A-proper topological degree has been given. Now, utilising the new concept, we give the corresponding definitions of convex A-proper, P*-compact and Pγ-compact in Menger PN-space. As an application of these new concepts, we prove the existence of solution for some equations.

The topological degree of A-proper mapping in the Menger PN-space (I)

In this paper, we introduce the concept of A-proper topological degree in Menger PN-space and study some of its properties. Utilising its properties, we obtain a new fixed point theorem.

Several nonlinear operator problems in the Menger PN space

In this paper, we investigate some nonlinear operator problems and the theory of topological degree. Meanwhile, we obtain some new fixed point theorems in the M-PN space.

On linearly topological structure and property of fuzzy normed linear space

In this paper, the simplified definition of fuzzy normed linear space is introduced; the different structure of fuzzy normed linear space with variable right norm R is discussed in terms of topological vector space, and its properties such as compactness, completeness and density are studied under more general left norm L and right norm R; as application, the linearly topological structure of Menger PN space is obtained.

On nonlinear equations for fuzzy mappings in probabilistic normed spaces

In this paper, we introduce the concept of probabilistic Ψ-contractor couple, which simplifies and weakens that of probabilistic Φ- g-contractor given by Cho et al. (Fuzzy Sets and Systems 110 (2000) 115–122). By using this concept, we study the existence and iteration convergence of solutions for set-valued nonlinear operator equations and nonlinear equations of fuzzy mappings in Menger PN-spaces. The results presented in this paper improve and extend the corresponding results of Cho et al. in a sense.

A note on probabilistic contractor couple and solutions for a system of nonlinear equations in n a menger pn-spaces

The concept of (ϕ , δ)-type probabilistic contractor couple was introduced which simplifies and weakens the definition of probabilistic contractor couple given by Zhang Shisheng. The existence and uniqueness of the solutions for a system of nonlinear operator equations with this kind of probabilistic contractor couple in N. A. Menger PN-spaces were studied. The works improve and extend the corresponding results by M. Altman, A. C. Lee, W. J. Padgett et at.

On probabilistic norm of a linear operators and space of operators

Since the PN space (E,F) which satisfies condition (PN-5) is just a Menger PN-space (E,F, min) the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting probabilistic norms of linear operators and spaces of operators are studied on more general Menger PN-spaces. The results presented improve and generalize the corresponding results by Xiao.

(?, ?)-Type probabilistic contractor and solutions for a nonlinear operator equations in Menger PN-spaces

The purpose of this paper is to introduce the concept of (Φ, Δ)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probablistic contractor in Menger PN-spaces. The results presented in this paper improve and extend the corresponding results in [1] and [4–8].

Some new fixed point theorems in probabilistic metric spaces

In this paper, we introduce the concept of the Z-M-PN space, and obtain some new fixed point theorems in probabilistic metric spaces. Meanwhile, some famous fixed point theorems are generalized in probabilistic metric spaces, such as fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.