Non-linear matrix integral equations of Volterra type in queueing theory

The use of a branching process argument in complex queueing situations often leads to a discussion of a non-linear matrix integral equation of Volterra type. By the use of a fixed point theorem we show these equations have a unique solution.

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On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

Journal of Applied Probability ◽

10.1017/s0021900200040900 ◽

1988 ◽

Vol 25 (02) ◽

pp. 257-267 ◽

Cited By ~ 5

Author(s):

D. Szynal ◽

S. Wedrychowicz

Keyword(s):

Banach Space ◽

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Stochastic Model ◽

Asymptotic Behaviour ◽

Existence Of Solutions ◽

Stochastic Integral ◽

Volterra Type ◽

Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

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A NONLINEAR F-CONTRACTION FORM OF SADOVSKII'S FIXED POINT THEOREM AND ITS APPLICATION TO A FUNCTIONAL INTEGRAL EQUATION OF VOLTERRA TYPE

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi200717024n ◽

2021 ◽

pp. 321

Author(s):

Kourosh Nourouzi ◽

Faezeh Zahedi ◽

Donal O'Regan

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Existence Of Solutions ◽

Functional Integral ◽

Volterra Type

In this paper, we give a nonlinear F-contraction form of the Sadovskii fixedpoint theorem and we also investigate the existence of solutions for a functional integral equation of Volterra type.

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The Boundary Value Problem with Haseman-shift for k-regular Functions on Unbounded Domains in Clifford Analysis

Journal of Mathematics Research ◽

10.5539/jmr.v8n1p38 ◽

2016 ◽

Vol 8 (1) ◽

pp. 38

Author(s):

Yan Zhang

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Unique Solution ◽

Clifford Analysis ◽

Boundary Value ◽

Regular Function ◽

Unbounded Domains ◽

Regular Functions

In this paper, we introduce the boundary value problem with Haseman shift for $k$-regular function on unbounded domains, and give the unique solution for this problem by integral equation<br />method and fixed-point theorem.

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Existence of solutions of a class of stochastic Volterra integral equations with applications to chemotherapy

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s033427000001105x ◽

1999 ◽

Vol 41 (1) ◽

pp. 93-104 ◽

Cited By ~ 4

Author(s):

R. Subramaniam ◽

K. Balachandran

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Stochastic Model ◽

Measure Of Noncompactness ◽

Existence Of Solutions ◽

Stochastic Integral ◽

Volterra Type ◽

Stochastic Integral Equation ◽

The Fixed Point Theorem

AbstractIn this paper we establish the existence of solutions of a more general class of stochastic integral equation of Volterra type. The main tools used here are the measure of noncompactness and the fixed point theorem of Darbo. The results generalize the results of Tsokos and Padgett [9] and Szynal and Wedrychowicz [7]. An application to a stochastic model arising in chemotherapy is discussed.

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On solutions of a stochastic integral equation of the volterra type with applications for chemotherapy

Journal of Applied Probability ◽

10.2307/3214434 ◽

1988 ◽

Vol 25 (2) ◽

pp. 257-267 ◽

Cited By ~ 5

Author(s):

D. Szynal ◽

S. Wedrychowicz

Keyword(s):

Banach Space ◽

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Stochastic Model ◽

Asymptotic Behaviour ◽

Existence Of Solutions ◽

Stochastic Integral ◽

Volterra Type ◽

Stochastic Integral Equation

This paper deals with the existence of solutions of a stochastic integral equation of the Volterra type and their asymptotic behaviour. Investigations of this paper use the concept of a measure of non-compactness in Banach space and fixed-point theorem of Darbo type. An application to a stochastic model for chemotherapy is also presented.

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Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity

Canadian Mathematical Bulletin ◽

10.4153/cmb-2011-123-5 ◽

2013 ◽

Vol 56 (1) ◽

pp. 80-91

Author(s):

Muhammad N. Islam

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Fixed Point Theorem ◽

Periodic Solutions ◽

Point Theorem ◽

Fixed Point Theorems ◽

Direct Method ◽

Banach Fixed Point Theorem ◽

Volterra Type ◽

Type Integral

AbstractIn this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's and Schaefer's fixed point theorems are employed in the analysis. The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions. We employ Liapunov's direct method to obtain such an a priori bound. In the process, we compare these theorems in terms of assumptions and outcomes.

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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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EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.10.6.2 ◽

2021 ◽

Vol 10 (6) ◽

pp. 2687-2710

Author(s):

F. Akutsah ◽

A. A. Mebawondu ◽

O. K. Narain

Keyword(s):

Integral Equation ◽

Fixed Point ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Existence Of Solution ◽

Volterra Type ◽

Complete Metric Spaces ◽

Type Integral ◽

New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

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