scholarly journals On existence of extremal solutions of nonlinear functional integral equations in Banach algebras

2004 ◽  
Vol 2004 (3) ◽  
pp. 271-282 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Simple Method ◽  
Nonlinear Functional ◽  
Equations Of Mixed Type ◽  
Special Cases ◽  
Functional Integral Equations

An algebraic fixed point theorem involving the three operators in a Banach algebra is proved using the properties of cones and they are further applied to a certain nonlinear integral equations of mixed type x(t)=k(t,x(μ(t)))+[f(t,x(θ(t)))](q(t)+∫0σ(t)v(t,s)g(s,x(η(s)))ds) for proving the existence of maximal and minimal solutions. Our results include the earlier fixed point theorems of Dhage (1992 and 1999) as special cases with a different but simple method.

scholarly journals On the solutions of a class of nonlinear integral equations in cone $b$-metric spaces over Banach algebras

2019 ◽  
Vol 11 (1) ◽  
pp. 163-178
Author(s):  
L.T. Quan ◽  
T. Van An
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Spaces ◽  
Banach Algebras ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Comparison Functions ◽  
Functional Integral Equations

In this paper, we study the existence of the solutions of a class of functional integral equations by using some fixed point results in cone $b$-metric spaces over Banach algebras. In order to obtain these results we introduced and proved some properties of generalized weak $\varphi$-contractions, in which the $\varphi$ are nonlinear weak comparison functions. The obtained results are generalizations of results of Van Dung N., Le Hang V. T., Huang H., Radenovic S. and  Deng G. Also, some suitable examples are given to illustrate obtained results.

scholarly journals On the Solutions of a Class of Nonlinear Integral Equations in the Banach Algebra of the Continuous Functions and Some Examples

2014 ◽  
Vol 52 (1) ◽  
Author(s):  
Ismet Özdemir ◽  
Bekir Ilhan ◽  
Ümit Çakan
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Continuous Functions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Bounded Interval ◽  
Special Cases ◽  
Functional Integral Equations

AbstractIn this paper, we study the existence of the solutions of a class of functional integral equations which contain a lot of classical nonlinear integral equations as special cases. We consider the solvability of the equations in the Banach algebra of continuous functions on a closed and bounded interval. The main tools here are the measure of noncompactness and the suitable fixed point theorem for the product of two operators in the Banach algebra.

scholarly journals The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Józef Banaś ◽  
Szymon Dudek
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Half Axis ◽  
Functional Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.

scholarly journals Further results on the existence of solutions for generalized fractional quadratic functional integral equations

2020 ◽  
Vol 1 (1) ◽  
pp. 33-46
Author(s):  
Mohammed S. Abdo
Keyword(s):  
Integral Equations ◽  
Existence Of Solutions ◽  
Continuous Solution ◽  
Functional Integral ◽  
Existence Results ◽  
Quadratic Functional ◽  
Nonlinear Functional Analysis ◽  
Nonlinear Functional ◽  
Special Cases ◽  
Functional Integral Equations

This paper discusses some existence results for at least one continuous solution for generalized fractional quadratic functional integral equations. Some results on nonlinear functional analysis including Schauder fixed point theorem are applied to establish the existence result for proposed equations. We improve and extend the literature by incorporated some well-known and commonly cited results as special cases in this topic. Further, we prove the existence of maximal and minimal solutions for these equations.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

On a generalized coupled fixed point theorem in C[0, 1] and its application to a class of coupled systems of functional-integral equations

2015 ◽  
Vol 31 (3) ◽  
pp. 333-337
Author(s):  
J. HARJANI ◽  
◽  
J. ROCHA ◽  
K. SADARANGANI ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Coupled Fixed Point ◽  
General System ◽  
Functional Integral ◽  
Coupled Systems ◽  
Nonlinear Functional ◽  
Coupled Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we present a result about the existence of a generalized coupled fixed point in the space C[0, 1]. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in C[0, 1] for a general system of nonlinear functional-integral equations with maximum.

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 The solvability of a class of system of nonlinear integral equations via measure of noncompactness

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5969-5991 ◽  
Author(s):  
Habibollah Nasiri ◽  
Jamal Roshan
Keyword(s):  
Fixed Points ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
General System ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Nonlinear Functional ◽  
Functional Integral Equations ◽  
Class Of Functions

We propose a new notion of contraction mappings for two class of functions involving measure of noncompactness in Banach space. In this regard we present some theory and results on the existence of tripled fixed points and some basic Darbo?s type fixed points for a class of operators in Banach spaces. Also as an application we discuss the existence of solutions for a general system of nonlinear functional integral equations which satisfy in new certain conditions. Further we give an example to verify the effectiveness and applicability of our results.

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