The concept of (Phi, Delta)-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 t...The concept of (Phi, Delta)-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 propabilistic 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 al.展开更多
The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such ...The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].展开更多
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this cont...Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.展开更多
In the present paper we use a control function to define a generalized contraction in Menger spaces and obtain a unique fixed point theorem. The work is in line with the research for developing probabilistic contracti...In the present paper we use a control function to define a generalized contraction in Menger spaces and obtain a unique fixed point theorem. The work is in line with the research for developing probabilistic contractions with the help of control functions and related fixed point results. We have given an example to which our theorem is applicable. Some corollaries are also discussed.展开更多
In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existe...In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.展开更多
In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.
In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Ha...In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.展开更多
In this paper, first, we introduce the notion of weakly compatible maps for coupled maps and then prove a coupled fixed point theorem under more general t-norm(H-type norm) in Menger spaces. We support our theorem by ...In this paper, first, we introduce the notion of weakly compatible maps for coupled maps and then prove a coupled fixed point theorem under more general t-norm(H-type norm) in Menger spaces. We support our theorem by providing a suitable example. At the end, we obtain an application.展开更多
In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the result...In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.展开更多
In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger sp...In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.展开更多
文摘The concept of (Phi, Delta)-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 propabilistic 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 al.
文摘The purpose of this paper is to introduce the coneept of (Φ,△)-type probabilistic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with such probabilistic contractor in Menger PN-spaces.The results presented in this paper improve and extend the corresponding results in [1] and [4-8].
文摘Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.
文摘In the present paper we use a control function to define a generalized contraction in Menger spaces and obtain a unique fixed point theorem. The work is in line with the research for developing probabilistic contractions with the help of control functions and related fixed point results. We have given an example to which our theorem is applicable. Some corollaries are also discussed.
基金Supported by the National Natural Science Foundation of China (10761007)
文摘In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.
文摘In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.
文摘In this paper, we introduce generalized cyclic C-contractions through p number of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.
文摘In this paper, first, we introduce the notion of weakly compatible maps for coupled maps and then prove a coupled fixed point theorem under more general t-norm(H-type norm) in Menger spaces. We support our theorem by providing a suitable example. At the end, we obtain an application.
基金Project supported by the Natural Science Foundation of Yibin University (No. 2009Z01)
文摘In this paper, first introduce and define an intuitionistic Menger inner product space, and then, obtain a new fixed point theorem in a complete intuitionistic Menger inner product space. As an application, the results are used to study the existence and uniqueness of the solution to a linear Volterra integral equation.
文摘In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.
