scholarly journals Solvability of functional stochastic integral equations via Darbo’s fixed point theorem

2021 ◽  
Vol 60 (6) ◽  
pp. 5631-5636
Author(s):  
Amar Deep ◽  
Syed Abbas ◽  
Bhupander Singh ◽  
M.R. Alharthi ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Stochastic Integral ◽  
Darbo’S Fixed Point Theorem ◽  
Stochastic Integral Equations

scholarly journals On solutions of general nonlinear stochastic integral equations

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
General Class ◽  
Stochastic Integral ◽  
Banach Fixed Point Theorem ◽  
Stochastic Integral Equations

We study the existence, uniqueness, and stability of random solutions of a general class of nonlinear stochastic integral equations by using the Banach fixed point theorem. The results obtained in this paper generalize the results of Szynal and Wędrychowicz (1993).

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

Simulation functions and Meir–Keeler condensing operators with application to integral equations

2021 ◽  
Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Darbo’S Fixed Point Theorem ◽  
Simulation Functions ◽  
Condensing Operators

We propose a new concept of condensing operators by using a notion of measure of non-compactness in the setting of Banach spaces and establish a new generalization of Darbo’s fixed point theorem. We also show the applicability of our results to integral equations. A concrete example will be presented to support the application part.

Global solutions for Volterra ordinary and retarded integral equations

2008 ◽  
Vol 41 (3) ◽  
Author(s):  
Bianca Satco
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integral Equations ◽  
Point Theorem ◽  
Global Solutions ◽  
Volterra Type ◽  
Darbo’S Fixed Point Theorem ◽  
Type Integral

AbstractUsing a generalization of Darbo’s fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [

scholarly journals Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 492
Author(s):  
Babak Mohammadi ◽  
Ali Asghar Shole Haghighi ◽  
Maryam Khorshidi ◽  
Manuel De la Sen ◽  
Vahid Parvaneh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals On New Extensions of Darbo’s Fixed Point Theorem with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 424 ◽  
Author(s):  
Hüseyin Işık ◽  
Shahram Banaei ◽  
Farhan Golkarmanesh ◽  
Vahid Parvaneh ◽  
Choonkil Park ◽  
...  
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

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