scholarly journals On the solvability of nonlinear integral equations in Lebesgue space

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 203-209
Author(s):  
E.M. El-Abd
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Lebesgue Space ◽  
Nonlinear Integral Equation ◽  
Basic Tool ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
The Fixed Point Theorem

In this paper we prove theorems on the existence of integrable and monotonic solutions of nonlinear integral equation in Lebesgue Space. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to the so-called measure of weak noncompactness.

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.

scholarly journals On the solvability of some nonlinear functional integral equations on Lp(R+)

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1841-1850
Author(s):  
Mahmoud Bousselsal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Basic Tool ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to so called measure of noncompactness. The obtained results generalize and extend several ones obtained earlier in many papers and monographs. An example which shows the applicability of our results is also included.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence 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 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 Measure of Weak Noncompactness and Fixed Point Theorems in Banach Algebras with Applications

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 130
Author(s):  
Mohamed Amine Farid ◽  
Karim Chaira ◽  
El Miloudi Marhrani ◽  
Mohamed Aamri
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Weak Topology ◽  
Fixed Point Theorems ◽  
Nonlinear Integral Equation ◽  
Nonlinear Operator ◽  
Banach Algebras ◽  
Measure Of Weak Noncompactness

In this paper, we prove some fixed point theorems for the nonlinear operator A · B + C in Banach algebra. Our fixed point results are obtained under a weak topology and measure of weak noncompactness; and we give an example of the application of our results to a nonlinear integral equation in Banach algebra.

scholarly journals Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

2019 ◽  
Vol 9 (1) ◽  
pp. 1187-1204
Author(s):  
Agnieszka Chlebowicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Function Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Half Axis ◽  
Suitable Measure

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

scholarly journals Coupled Optimal Results with an Application to Nonlinear Integral Equations

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 73
Author(s):  
Pulak Konar ◽  
Sumit Chandok ◽  
Shrutinil Dutta ◽  
Manuel De la Sen
Keyword(s):  
Integral Equation ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonlinear Integral Equation ◽  
Nonlinear Integral Equations ◽  
Control Functions ◽  
Coupled Fixed Points

In the present work, we consider the best proximal problem related to a coupled mapping, which we define using control functions and weak inequalities. As a consequence, we obtain some results on coupled fixed points. Our results generalize some recent results in the literature. Also, as an application of the results obtained, we present the solution to a system of a coupled Fredholm nonlinear integral equation. Our work is supported by several illustrations.

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