A continuum of solutions in a Fréchet space of a nonlinear functional integral equation in N variables

2016 ◽  
Vol 289 (13) ◽  
pp. 1665-1679 ◽  
Author(s):  
Le Thi Phuong Ngoc ◽  
Nguyen Thanh Long
Keyword(s):  
Integral Equation ◽  
Functional Integral ◽  
Fréchet Space ◽  
Frechet Space ◽  
Nonlinear Functional

Existence and global attractivity of solutions of a nonlinear functional integral equation

2010 ◽  
Vol 216 (1) ◽  
pp. 261-268 ◽  
Author(s):  
Józef Banaś ◽  
Krishnan Balachandran ◽  
Diana Julie
Keyword(s):  
Integral Equation ◽  
Global Attractivity ◽  
Functional Integral ◽  
Nonlinear Functional

scholarly journals Global Asymptotic Stability for Nonlinear Functional Integral Equation of Mixed Type

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhinan Xia
Keyword(s):  
Integral Equation ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Mixed Type ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Equation Of Mixed Type ◽  
Stability Of The Solution

The existence results of global asymptotic stability of the solution are proved for functional integral equation of mixed type. The measure of noncompactness and the fixed-point theorem of Darbo are the main tools in carrying out our proof. Furthermore, some examples are given to show the efficiency and usefulness of the main findings.

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 On the solvability of a nonlinear functional integral equations via measure of noncompactness in

2020 ◽  
Vol 19 ◽  
pp. 74-88
Author(s):  
Wagdy G. El-Sayed ◽  
Mahmoud M. El-Borai ◽  
Mohamed M.A. Metwali ◽  
Nagwa I. Shemais
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Abstract Result ◽  
Nonlinear Functional ◽  
Darbo Fixed Point Theorem ◽  
Integrable Functions ◽  
Functional Integral Equations ◽  
Suitable Measure

Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions Lp(RN). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result.

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