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 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>

scholarly journals The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2130
Author(s):  
Hasanen A. Hammad ◽  
Amal A. Khalil
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Integral Equations ◽  
Linear Functional ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
General Class Of Functions ◽  
Functional Integral Equations ◽  
Class Of Functions

Under the idea of a measure of noncompactness, some fixed point results are proposed and a generalization of Darbo’s fixed point theorem is given in this manuscript. Furthermore, some novel quadruple fixed points results via a measure of noncompactness for a general class of functions are presented. Ultimately, the solutions to a system of non-linear functional integral equations by the fixed point results obtained are discussed, and non-trivial examples to illustrate the validity of our study are derived.

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.

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