A multiparametric family of solutions to a singular Volterra integral equation in a Banach space

2011 ◽  
Vol 55 (1) ◽  
pp. 50-61
Author(s):  
I. V. Sapronov
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

scholarly journals On a Fredholm-Volterra integral equation

2021 ◽  
Vol 66 (3) ◽  
pp. 567-573
Author(s):  
Alexandru-Darius Filip ◽  
Ioan A. Rus
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Unique Solution ◽  
Iterative Algorithm ◽  
Volterra Integral Equation ◽  
Complex Banach Space

"In this paper we give conditions in which the integral equation $$x(t)=\displaystyle\int_a^c K(t,s,x(s))ds+\int_a^t H(t,s,x(s))ds+g(t),\ t\in [a,b],$$ where $a<c<b$, $K\in C([a,b]\times [a,c]\times \mathbb{B},\mathbb{B})$, $H\in C([a,b]\times [a,b]\times \mathbb{B},\mathbb{B})$, $g\in C([a,b],\mathbb{B})$, with $\mathbb{B}$ a (real or complex) Banach space, has a unique solution in $C([a,b],\mathbb{B})$. An iterative algorithm for this equation is also given."

LINEAR INTEGRAL VOLTERRA EQUATION OF THE FIRST KIND IN THE BANACH SPACE

2015 ◽  
Vol 4 (2) ◽  
pp. 8-13
Author(s):  
Зенина ◽  
V. Zenina ◽  
Сапронов ◽  
Ivan Sapronov ◽  
Уточкина ◽  
...  
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation ◽  
Volterra Equation ◽  
Polynomial Kernel ◽  
Integral Volterra Equation ◽  
Integrable Functions ◽  
Linear Integral ◽  
Space Of Integrable Functions

We construct solutions to a singular Volterra integral equation of the first kind with а polynomial kernel in the space of integrable functions whose values be-long to a Banach space.

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