Some Theorems in the Existence, Uniqueness and Stability solutions of Volterra Integrals Equations (original) (raw)

On Global Existence Theorem of Certain Volterra Integral Equation of Second Kind

Journal of Bangladesh Academy of Sciences, 2012

The aim of the paper was to fabricate an alternative proof of a global existence theorem of certain type of Volterrea integral equation on the basis of the hypothesis. The new proof has been given by constructing suitable function space and using fixed point theorem. Relaxing some hypotheses in the same and using Bielecki's notion of norm another global existence theorem has been proposed and proved.

Solvability and numerical method for non-linear Volterra integral equations by using Petryshyn’s fixed point theorem

International Journal of Nonlinear Analysis and Applications, 2022

In this paper, utilizing the technique of Petryshyn’s fixed point theorem in Banach algebra, we analyze the existence of solution for functional integral equations, which includes as special cases many functional integral equations that arise in various branches of non-linear analysis and its application. Finally, we introduce the numerical method formed by modified homotopy perturbation approach to resolving the problem with acceptable accuracy.

On the Ulam Type Stability of Nonlinear Volterra Integral Equations

arXiv (Cornell University), 2021

In this paper, we examine the Hyers-Ulam and Hyers-Ulam-Rassias stability of solutions of a general class of nonlinear Volterra integral equations. By using a fixed point alternative and improving a technique commonly used in similar problems, we extend and improve some well-known results on this problem. We also provide some examples visualizing the improvement of the results mentioned.

Qualitative Properties of Nonlinear Volterra Integral Equations

2008

In this article, the contraction mapping principle and Liapunov's method are used to study qualitative properties of nonlinear Volterra equations of the form x(t) = a(t) Z t 0 C(t,s)g(s,x(s)) ds,t � 0. In particular, the existence of bounded solutions and solutions with various Lp properties are studied under suitable conditions on the functions involved with this equation.

EXISTENCE AND UNIQUENESS RESULTS FOR VOLTERRA-FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

Advances in the Theory of Nonlinear Analysis and its Applications, 2020

This paper establishes a study on some important latest innovations in the existence and uniqueness results by means of Banach contraction xed point theorem for Caputo fractional Volterra-Fredholm integro-dierential equations with boundary condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented.