Fixed point theorems in the Fréchet space and functional integral equations on an unbounded interval

2012 ◽  
Vol 218 (18) ◽  
pp. 9066-9074 ◽  
Author(s):  
Leszek Olszowy
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Functional Integral ◽  
Fréchet Space ◽  
Frechet Space ◽  
Unbounded Interval ◽  
Functional Integral Equations

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

scholarly journals Application of measure of noncompactness for the system of functional integral equations

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3063-3073 ◽  
Author(s):  
Reza Arab
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Darbo Fixed Point Theorem ◽  
Functional Integral Equations

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banch space via the measure of non-compactness, which generalize the result of Aghajani et al.[6]. Our results generalize, extend, and unify several well-known comparable results in the literature. As an application, we study the existence of solutions for the system of integral equations.

scholarly journals Compactness Conditions in the Study of Functional, Differential, and Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Józef Banaś ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Functional Differential ◽  
Functional Integral Equations ◽  
Differential And Integral Equations

We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactness conditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel’skii-Burton, and Schaefer. We present also the technique associated with measures of noncompactness and we illustrate its applicability in proving the solvability of some functional integral equations. Apart from this, we discuss the application of the mentioned technique to the theory of ordinary differential equations in Banach spaces.

Existence of tripled fixed points and solution of functional integral equations through a measure of noncompactness

2019 ◽  
Vol 35 (2) ◽  
pp. 193-208
Author(s):  
HABIB UR REHMAN ◽  
POOM KUMAM ◽  
SOMPONG DHOMPONGSA ◽  
◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
General System ◽  
Functional Integral ◽  
Tripled Fixed Point ◽  
General Class Of Functions ◽  
Functional Integral Equations ◽  
Class Of Functions

In this paper, we propose fixed point results through the notion of a measure of noncompactness and give a generalization of a Darbo’s fixed point theorem. We also prove some new tripled fixed point results via a measure of noncompactness for a more general class of functions. Our results generalize and extend some comparable results in the literature. Further, we apply the obtained fixed point theorems to prove the existence of solutions for a general system of non-linear functional integral equations. In the end, an example is given to illustrate the validity of our results.

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.

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.

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