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).

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 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 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 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>

Asymptotic stability of solutions for a class of nonlinear functional integral equations of fractional order

2016 ◽  
Vol 53 (2) ◽  
pp. 256-288
Author(s):  
Ümit Çakan ◽  
İsmet Özdemir
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Asymptotically Stable ◽  
Stability Of Solutions ◽  
Nonlinear Functional ◽  
Bounded Functions ◽  
Stable Solutions ◽  
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 asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.

scholarly journals Existence of Solution for Non-Linear Functional Integral Equations of Two Variables in Banach Algebra

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 674 ◽  
Author(s):  
Hari M. Srivastava ◽  
Anupam Das ◽  
Bipan Hazarika ◽  
S. A. Mohiuddine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Algebra ◽  
Integral Equations ◽  
Point Theorem ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Non Linear ◽  
Functional Integral Equations

The aim of this article is to establish the existence of the solution of non-linear functional integral equations x ( l , h ) = U ( l , h , x ( l , h ) ) + F l , h , ∫ 0 l ∫ 0 h P ( l , h , r , u , x ( r , u ) ) d r d u , x ( l , h ) × G l , h , ∫ 0 a ∫ 0 a Q l , h , r , u , x ( r , u ) d r d u , x ( l , h ) of two variables, which is of the form of two operators in the setting of Banach algebra C [ 0 , a ] × [ 0 , a ] , a > 0 . Our methodology relies upon the measure of noncompactness related to the fixed point hypothesis. We have used the measure of noncompactness on C [ 0 , a ] × [ 0 , a ] and a fixed point theorem, which is a generalization of Darbo’s fixed point theorem for the product of operators. We additionally illustrate our outcome with the help of an interesting example.

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.

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