scholarly journals A Digital Version of the Kakutani Fixed Point Theorem for Convex-valued Multifunctions

2001 ◽  
Vol 40 ◽  
pp. 393-407 ◽  
Author(s):  
Michael B. Smyth ◽  
Rueiher Tsaur
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Digital Version ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

scholarly journals Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonlinear Operator ◽  
Wage Equation ◽  
Short Run ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

Each short-run equilibrium of the Dixit-Stiglitz-Krugman model is defined as a solution to the wage equation when the distributions of workers and farmers are given functions. We extend the discrete nonlinear operator contained in the wage equation as a set-valued operator. Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.

scholarly journals On a Multivalued Differential Equation with Nonlocality in Time

2020 ◽  
Vol 48 (4) ◽  
pp. 703-718
Author(s):  
André Eikmeier ◽  
Etienne Emmrich
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Growth Conditions ◽  
The Other ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Volterra Integral Operator ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

AbstractThe initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of convolution type with exponential decay. The two operators act on different Banach spaces where one is not embedded in the other. The set-valued right-hand side is measurable and satisfies certain continuity and growth conditions. Existence of a solution is shown via a generalisation of the Kakutani fixed-point theorem.

Sign in / Sign up

Export Citation Format

Share Document