Applying a fixed point theorem of Krasnosel’skii type to the existence of asymptotically stable solutions for a Volterra–Hammerstein integral equation

2011 ◽  
Vol 74 (11) ◽  
pp. 3769-3774 ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Asymptotically Stable ◽  
Hammerstein Integral Equation ◽  
Stable Solutions

Positive solutions of perturbed nonlinear hammerstein integral equation

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Aneta Sikorska-Nowak ◽  
Mirosława Zima
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Perturbation ◽  
Hammerstein Integral Equation ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractWe discuss the existence of positive solutions for the nonlinear perturbation of Hammerstein integral equation. The technique we use is based on the fixed point theorem of Leggett-Williams type for strict set contractions. We conclude the paper by providing some examples that illustrate our claim.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

A new extension of Kannan’s fixed point theorem via F-contraction with application to integral equations

2021 ◽  
pp. 2250123
Author(s):  
Pradip Debnath
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Extended Version

Our aim is to introduce an updated and real generalization of Kannan’s fixed point theorem with the help of [Formula: see text]-contraction introduced by Wardowski for single-valued mappings. Our result can be useful to ascertain the existence of fixed point for a family of mappings for which neither the Wardowski’s result nor that of Kannan can be applied directly. Our result has been applied to solve a particular type of integral equation. Finally, we establish a Reich-type extended version of the main result.

scholarly journals An Application of Random Fixed Point Theorem in Integral Equation

2014 ◽  
Vol 9 (4) ◽  
pp. 57-61
Author(s):  
Mukti Gangopadhyay ◽  
◽  
Pritha Dan ◽  
M. Saha
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Random Fixed Point ◽  
Random Fixed Point Theorem

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

scholarly journals The Newtonian Operator and Global Convergence Balls for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1074
Author(s):  
José A. Ezquerro ◽  
Miguel A. Hernández-Verón
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Convergence ◽  
Point Theorem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Integral Equation ◽  
The Fixed Point Theorem ◽  
Linear Integral

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

scholarly journals An Extension of Darbo’s Theorem and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. Samadi ◽  
M. B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo Fixed Point Theorem ◽  
Real Functions

Here, some extensions of Darbo fixed point theorem associated with measures of noncompactness are proved. Then, as an application, our attention is focused on the existence of solutions of the integral equationx(t)=F(t,f(t,x(α1(t)),  x(α2(t))),((Tx)(t)/Γ(α))×∫0t‍(u(t,s,max⁡[0,r(s)]⁡|x(γ1(τ))|,  max⁡[0,r(s)]⁡|x(γ2(τ))|)/(t-s)1-α)ds,  ∫0∞v(t,s,x(t))ds),    0<α≤1,t∈[0,1]in the space of real functions defined and continuous on the interval[0,1].

scholarly journals On Pata–Suzuki-Type Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 720
Author(s):  
Obaid Alqahtani ◽  
Venigalla Madhulatha Himabindu ◽  
Erdal Karapınar
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Metric Space ◽  
Complete Metric Space ◽  
Admissible Mapping

In this paper, we aim to obtain fixed-point results by merging the interesting fixed-point theorem of Pata and Suzuki in the framework of complete metric space and to extend these results by involving admissible mapping. After introducing two new contractions, we investigate the existence of a (common) fixed point in these new settings. In addition, we shall consider an integral equation as an application of obtained results.

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