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 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.

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 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 Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

2019 ◽  
Vol 52 (1) ◽  
pp. 166-182 ◽  
Author(s):  
Habib ur Rehman ◽  
Dhananjay Gopal ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Darbo’S Fixed Point Theorem ◽  
Condensing Operators ◽  
Functional Integral Equations

AbstractIn this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we defineα-ψandβ-ψcondensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

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