A fixed point theorem, a perturbed differential equation, and a multivariable Volterra integral equation

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.

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Applications of a Fixed Point Result for Solving Nonlinear Fractional and Integral Differential Equations

Fractal and Fractional ◽

10.3390/fractalfract5040211 ◽

2021 ◽

Vol 5 (4) ◽

pp. 211

Author(s):

Liliana Guran ◽

Zoran D. Mitrović ◽

G. Sudhaamsh Mohan Reddy ◽

Abdelkader Belhenniche ◽

Stojan Radenović

Keyword(s):

Differential Equation ◽

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Fractional Differential Equation ◽

Point Theorem ◽

Existence Of Solutions ◽

Fractional Differential ◽

Integral Differential Equations

In this article, we apply one fixed point theorem in the setting of b-metric-like spaces to prove the existence of solutions for one type of Caputo fractional differential equation as well as the existence of solutions for one integral equation created in mechanical engineering.

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Fixed point theorem on volterra integral equation

Journal of Physics Conference Series ◽

10.1088/1742-6596/1375/1/012064 ◽

2019 ◽

Vol 1375 ◽

pp. 012064

Author(s):

S C Sihombing ◽

L Lia

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Volterra Integral Equation

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

Filomat ◽

10.2298/fil1812341h ◽

2018 ◽

Vol 32 (12) ◽

pp. 4341-4350 ◽

Cited By ~ 1

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.

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

Iraqi Journal of Science ◽

10.24996/ijs.2020.61.s.i.16 ◽

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,∞).

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

Journal of the Australian Mathematical Society ◽

10.1017/s144678870001003x ◽

1972 ◽

Vol 14 (2) ◽

pp. 182-199 ◽

Cited By ~ 2

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 ≦.

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

International Journal of Analysis ◽

10.1155/2014/280709 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

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.

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A new extension of Kannan’s fixed point theorem via F-contraction with application to integral equations

Asian-European Journal of Mathematics ◽

10.1142/s1793557122501236 ◽

2021 ◽

pp. 2250123

Author(s):

Pradip Debnath

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Integral Equations ◽

Point Theorem ◽

Extended Version

Our aim is to introduce an updated and real generalization of Kannan’s fixed point theorem with the help of [Formula: see text]-contraction introduced by Wardowski for single-valued mappings. Our result can be useful to ascertain the existence of fixed point for a family of mappings for which neither the Wardowski’s result nor that of Kannan can be applied directly. Our result has been applied to solve a particular type of integral equation. Finally, we establish a Reich-type extended version of the main result.

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Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

Abstract and Applied Analysis ◽

10.1155/2012/540846 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15

Author(s):

Yang Liu ◽

Zhang Weiguo

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Nonlinear Differential Equation ◽

Positive Solutions ◽

Fractional Order ◽

Point Theorem ◽

Boundary Value ◽

Order Derivative ◽

Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

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