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

2012 ◽  
Vol 36 (2) ◽  
pp. 147-152
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
AFM Khodadad Khan
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Existence Theorem ◽  
Function Space ◽  
Volterra Integral Equation ◽  
Alternative Proof ◽  
Global Existence Theorem ◽  
Academy Of Sciences

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. DOI: http://dx.doi.org/10.3329/jbas.v36i2.12956 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 2, 147-152, 2012

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 Solution of Volterra integral equation in metric spaces via new fixed point theorem

Filomat ◽  
2018 ◽  
Vol 32 (12) ◽  
pp. 4341-4350 ◽  
Author(s):  
Nawab Hussain ◽  
Eqal Al-Mazrooei ◽  
Abdul Khan ◽  
Jamshaid Ahmad
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Special Cases

The aim of this article is to study the existence of coincidences and fixed points of generalized hybrid contractions involving single-valued mappings and left total relations in the context of complete metric spaces. Some special cases are also discussed to derive some well known results of the literature. Finally, some examples and applications are also presented to verify the effectiveness and applicability of our main results.

scholarly journals On Existence and Uniqueness of an Integrable Solution for a Fractional Volterra Integral Equation on 𝑹+

2020 ◽  
pp. 122-125
Author(s):  
Faez N. Ghaffoori
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Uniqueness Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Theorem ◽  
Integrable Solution

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

scholarly journals Convolution, fixed point, and approximation in Stieltjes-Volterra integral equations

1972 ◽  
Vol 14 (2) ◽  
pp. 182-199 ◽  
Author(s):  
Carl W. Bitzer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
The Other ◽  
Integral Equation Theory ◽  
Identity Function ◽  
Convolution Integrals

This paper focuses primarily on two aspects of Stieltjes-Volterra integral equation theory. One is a theory for convolution integrals — that is, integrals of the form — and the other is a fixed point theorem for a mapping which is induced by an integral equation. Throughout the paper I will denote the identity function whose range of definition should be clear from the context and all integrals will be left integrals, written , whose simplest approximating sum is [f(b) – f(a)]·g(a) and whose value is the limit of approximating sums with respect to successive refinements of the interval. Also, N will denote the set of elements of a complete normed ring with unity 1 and S will denote a set linearly ordered by ≦.

scholarly journals Integrable Solutions of a Nonlinear Integral Equation via Noncompactness Measure and Krasnoselskii's Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mahmoud Bousselsal ◽  
Sidi Hamidou Jah
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Nonlinear Integral Equations ◽  
Measure Of Weak Noncompactness ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Noncompactness Measure

We study the existence of solutions of a nonlinear Volterra integral equation in the space L1[0,+∞). With the help of Krasnoselskii’s fixed point theorem and the theory of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes on nonlinear integral equations. Our results extend and generalize some previous works. An example is given to support our results.

scholarly journals GLOBAL EXISTENCE RESULTS FOR FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH STATE-DEPENDENT DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Mouffak Benchohra ◽  
Johnny Henderson ◽  
Imene Medjadj
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential ◽  
Functional Differential Inclusions

Our aim in this work is to study the existence of solutions of a functional differential inclusion with state-dependent delay. We use the Bohnenblust–Karlin fixed point theorem for the existence of solutions.

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