An Observation Concerning the Application of the Contraction-Mapping Fixed-Point Theorem, and a Result Concerning the Norm-Boundedness of Solutions of Nonlinear Functional Equations

1965 ◽  
Vol 44 (8) ◽  
pp. 1809-1812 ◽  
Author(s):  
I. W. Sandberg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Contraction Mapping ◽  
Boundedness Of Solutions ◽  
Nonlinear Functional

scholarly journals Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

2019 ◽  
Vol 52 (1) ◽  
pp. 166-182 ◽  
Author(s):  
Habib ur Rehman ◽  
Dhananjay Gopal ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo’S Fixed Point Theorem ◽  
Condensing Operators ◽  
Functional Integral Equations

AbstractIn this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we defineα-ψandβ-ψcondensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

2020 ◽  
Vol 102 (2) ◽  
pp. 293-302
Author(s):  
THEERAYOOT PHOCHAI ◽  
SATIT SAEJUNG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Functional Equations ◽  
Linear Functional ◽  
Linear Equations ◽  
General Linear ◽  
Several Variables ◽  
Linear Functional Equations

Zhang [‘On hyperstability of generalised linear functional equations in several variables’, Bull. Aust. Math. Soc.92 (2015), 259–267] proved a hyperstability result for generalised linear functional equations in several variables by using Brzdęk’s fixed point theorem. We complete and extend Zhang’s result. We illustrate our results for general linear equations in two variables and Fréchet equations.

Three Positive Periodic Solutions of Nonlinear Functional Differential Equations with Impulse Effects

2011 ◽  
Vol 403-408 ◽  
pp. 1319-1321
Author(s):  
Lei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Functional Differential Equations ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

In this paper, a type of nonlinear functional differential equations with impulse effects are studied by using the Leggett-Williams fixed point theorem.

scholarly journals A Fixed Point Theorem of the Hardy and Rogers Kind Endowed with Multiplicative Cone-C Class Functions

2019 ◽  
pp. 169-179
Author(s):  
Clement Boateng Ampadu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Cone Metric Space ◽  
Open Problems ◽  
Cone Metric

In this paper we introduce the multiplicative version of cone-C class functions [1], and obtain some contraction mapping theorems of the Hardy and Rogers kind in multiplicative cone metric space endowed with such functions. Further, we propose some open problems that are publishable in nature.

scholarly journals On fixed point theorem in complete quasi-metric space under F-contraction mapping

2019 ◽  
Vol 24 (2) ◽  
pp. 88
Author(s):  
Rifaat Saad Abdul-Jabbar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Contraction Mapping ◽  
Subject Classification

In this paper, a fixed point theorem under F-contraction mapping was considered and proved in complete quasi-metric space. This theorem was considered by Piri and Kumam in [1]. Subject Classification : 30C45; 30C10; 47B38    http://dx.doi.org/10.25130/tjps.24.2019.037

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