An extension of Krugman’s core–periphery model to the case of a continuous domain: Existence and uniqueness of solutions of a system of nonlinear integral equations in spatial economics

2013 ◽  
Vol 14 (6) ◽  
pp. 2116-2132 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima ◽  
Yuusuke Sakai ◽  
Ichiro Takagi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Spatial Economics ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Continuous Domain

scholarly journals Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg ◽  
Poom Kumam
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Implicit Relation ◽  
Existence And Uniqueness Results ◽  
Contractive Mappings ◽  
Uniqueness Results ◽  
Relation Type

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.

scholarly journals Related fixed point results for cyclic contractions on G-metric spaces and application

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 853-869 ◽  
Author(s):  
Hassen Aydi ◽  
Abdelbasset Felhi ◽  
Slah Sahmim
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Cyclic Contractions

In this paper, we establish some fixed point theorems in G-metric spaces involving generalized cyclic contractions. Some subsequent results are derived. The presented results generalize many well known results in the literature. Moreover, we provide some concrete examples and an application on the existence and uniqueness of solutions to a class of nonlinear integral equations.

scholarly journals Nonlinear generalized cyclic contractions in complete G-metric spaces and applications to integral equations

2013 ◽  
Vol 18 (2) ◽  
pp. 160-176 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Cyclic Contractions

In this paper we introduce generalized cyclic contractions in G-metric spaces and establish some fixed point theorems. The presented theorems extend and unify various known fixed point results. Examples are given in the support of these results. Finally, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is given.

scholarly journals Fuzzy Volterra integral equations with in-finite delay

2009 ◽  
Vol 40 (1) ◽  
pp. 19-29 ◽  
Author(s):  
P. Prakash ◽  
V. Kalaiselvi
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Volterra Integral Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Finite Delay

In this paper, we study the existence and uniqueness of solutions for a class of fuzzy Volterra integral equations with infinite delay by using the method of successive approximations.

QUANTUM INTEGRAL EQUATIONS OF VOLTERRA TYPE WITH GENERALIZED OPERATOR-VALUED KERNELS

2000 ◽  
Vol 03 (04) ◽  
pp. 505-517 ◽  
Author(s):  
ZHIYUAN HUANG ◽  
CAISHI WANG ◽  
XIANGJUN WANG
Keyword(s):  
Integral Equation ◽  
Explicit Expression ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Uniqueness Of Solutions ◽  
Volterra Type ◽  
Quantum Integral ◽  
Generalized Operator

Quantum integral equation of Volterra type with generalized operator-valued kernel is introduced. Existence and uniqueness of solutions are established, explicit expression of the solution is given, the continuity, continuous dependence on free terms and other properties of the solution are proved.

scholarly journals The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

Sign in / Sign up

Export Citation Format

Share Document