scholarly journals On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces

1994 ◽  
Vol 17 (2) ◽  
pp. 389-396 ◽  
Author(s):  
Shih-Sen Chang ◽  
Yeol Je Cho ◽  
Fan Wang
Keyword(s):  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Normed Spaces ◽  
Uniqueness Of Solutions ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Probabilistic Normed Spaces

In this paper, we introduce the concept of more general probabilistic contractors in probabilistic normed spaces and show the existence and uniqueness of solutions for set-valued and single-valued nonlinear operator equations in Menger probabilistic normed spaces.

scholarly journals Fixed Point Theorems on Nonlinear Binary Operator Equations with Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Baomin Qiao
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Nonlinear Operator ◽  
Order Theory ◽  
Iteration Theory ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Monotone Iteration ◽  
Binary Operator

The existence and uniqueness for solution of systems of some binary nonlinear operator equations are discussed by using cone and partial order theory and monotone iteration theory. Furthermore, error estimates for iterative sequences and some corresponding results are obtained. Finally, the applications of our results are given.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

scholarly journals Iterations converging to distinct solutions of some nonlinear operator equations in Banach space

1986 ◽  
Vol 9 (3) ◽  
pp. 583-587
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Nonlinear Operator ◽  
Operator Equations ◽  
Nonlinear Operator Equations

We examine the solvability of multilinear equations of the formMk(x,x,…,x)−k   times−=y,   k=2,3,…whereMkis ak-linear operator on a Banach spaceXandy∈Xis fixed.

Sign in / Sign up

Export Citation Format

Share Document