The solvability of some nonlinear functional integral equations

2016 ◽  
Vol 53 (1) ◽  
pp. 7-21
Author(s):  
İsmet Özdemir ◽  
Ümit Çakan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Continuous Functions ◽  
Functional Integral ◽  
Space Of Continuous Functions ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable

scholarly journals On the Existence of the Solutions for Some Nonlinear Volterra Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
İsmet Özdemir ◽  
Ümit Çakan ◽  
Bekir İlhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Functional Integral ◽  
Space Of Continuous Functions ◽  
Nonlinear Functional ◽  
Functional Integral Equations

We present a theorem which gives sufficient conditions for existence of at least one solution for some nonlinear functional integral equations in the space of continuous functions on the interval[0,a]. To do this, we will use Darbo's fixed-point theorem associated with the measure of noncompactness. We give also an example satisfying the conditions of our main theorem but not satisfying the conditions described by Maleknejad et al. (2009).

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 existence theorem for nonlinear functional Volterra integral equations via Petryshyn's fixed point theorem

2022 ◽  
Vol 7 (4) ◽  
pp. 5594-5604
Author(s):  
Soniya Singh ◽  
◽  
Satish Kumar ◽  
Mohamed M. A. Metwali ◽  
Saud Fahad Aldosary ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Algebra ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Linear Analysis ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Functional Integral Equations

<abstract><p>Using the method of Petryshyn's fixed point theorem in Banach algebra, we investigate the existence of solutions for functional integral equations, which involves as specific cases many functional integral equations that appear in different branches of non-linear analysis and their applications. Finally, we recall some particular cases and examples to validate the applicability of our study.</p></abstract>

scholarly journals Solvability for generalized nonlinear two dimensional functional integral equations via measure of noncompactness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soniya Singh ◽  
Bhupander Singh ◽  
Kottakkaran Sooppy Nisar ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Two Dimensional ◽  
Functional Integral Equations

AbstractIn this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the corresponding results of several authors. We present fascinating examples of equations.

scholarly journals Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 214 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Control Function ◽  
Functional Integral ◽  
Existence Of A Solution ◽  
And Control ◽  
Functional Integral Equations

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

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.

scholarly journals Application of measure of noncompactness for the system of functional integral equations

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3063-3073 ◽  
Author(s):  
Reza Arab
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Darbo Fixed Point Theorem ◽  
Functional Integral Equations

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banch space via the measure of non-compactness, which generalize the result of Aghajani et al.[6]. Our results generalize, extend, and unify several well-known comparable results in the literature. As an application, we study the existence of solutions for the system of integral equations.

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