scholarly journals Extension of Darbo’s fixed point theorem via shifting distance functions and its application

2022 ◽  
Vol 27 ◽  
pp. 1-14
Author(s):  
Hemant Kumar Nashine ◽  
Anupam Das

In this paper, we discuss solvability of infinite system of fractional integral equations (FIE) of mixed type. To achieve this goal, we first use shifting distance function to establish a new generalization of Darbo’s fixed point theorem, and then apply it to the FIEs to establish the existence of solution on tempered sequence space. Finally, we verify our results by considering a suitable example.

2021 ◽  
Vol 6 (12) ◽  
pp. 13358-13369
Author(s):  
Rahul ◽  
◽  
Nihar Kumar Mahato

<abstract><p>In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.</p></abstract>


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Anupam Das ◽  
Iyad Suwan ◽  
Bhuban Chandra Deuri ◽  
Thabet Abdeljawad

AbstractThe aim of this paper is the solvability of generalized proportional fractional(GPF) integral equation at Banach space $\mathbb{E}$ E . Herein, we have established a new fixed point theorem which is then applied to the GPF integral equation in order to establish the existence of solution on the Banach space. At last, we have illustrated a genuine example that verified our theorem and gave a strong support to prove it.


2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad

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.


Author(s):  
Moosa Gabeleh ◽  
Mehdi Asadi ◽  
Pradip Ramesh Patle

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.


2019 ◽  
Vol 52 (1) ◽  
pp. 166-182 ◽  
Author(s):  
Habib ur Rehman ◽  
Dhananjay Gopal ◽  
Poom Kumam

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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