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 ≦.

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

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.

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 A random version of Schaefer's fixed point theorem with applications to functional random integral equations

2004 ◽  
Vol 35 (3) ◽  
pp. 197-206 ◽  
Author(s):  
B. C. Dhage
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Nonlinear Functional ◽  
Carathéodory Conditions ◽  
Random Integral

In this paper a random version of a fixed-point theorem of Schaefer is obtained and it is further applied to a certain nonlinear functional random integral equation for proving the existence result under Caratheodory conditions.

scholarly journals An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 879-886 ◽  
Author(s):  
A. Samadi ◽  
M.B. Ghaemi
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Coupled Fixed Point ◽  
Coupled Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

In this paper, an extension of Darbo fixed point theorem is introduced. By applying our extension, we obtain a coupled fixed point theorem and a solution for an integral equation. The proofs of our results are based on the technique of measure of noncompactness.

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 Generalization of Darbos fixed point theorem via SRμ-contractions with application to integral equations

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Farzad Zarinfar ◽  
Farshid Khojasteh ◽  
Mansour Vaezpour
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Current Paper ◽  
Simulation Function

The aim of the current paper is introducing a generalization of Darbo?s fixed point theorem based on SR-functions. In comparison with simulation function, SR-functions are able to cover the Meir-Keeler functions. Thus, the integral equations which are related to L-functions can be solved by our results. In the sequel, we find a solution for an integral equation to support our results.

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