A random integral equation of the volterra type

1971 ◽  
pp. 27-47
Author(s):  
Chris P. Tsokos ◽  
W. J. Padgett
Keyword(s):  
Integral Equation ◽  
Volterra Type ◽  
Random Integral

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

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.

scholarly journals On monotonic solutions of an integral equation of Volterra type

2005 ◽  
Vol 174 (1) ◽  
pp. 119-133 ◽  
Author(s):  
J. Caballero ◽  
J. Rocha ◽  
K. Sadarangani
Keyword(s):  
Integral Equation ◽  
Volterra Type

Lateral structure-foundation interaction of structures with base masses

1972 ◽  
Vol 62 (2) ◽  
pp. 453-470
Author(s):  
R. J. Scavuzzo ◽  
D. D. Raftopoulos ◽  
J. L. Bailey
Keyword(s):  
Integral Equation ◽  
Free Field ◽  
Response Spectra ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Transient Solution ◽  
Volterra Type ◽  
Seismic Motion ◽  
Lateral Structure ◽  
Inertia Forces

abstract The interaction of lateral inertia forces of an N-mass structure with a base mass and lateral seismic motion of the foundation is formulated as an integral equation of the Volterra type. Flexibility of the foundation is based on the transient solution of a two-dimensional elastic half-space. Interaction effects are evaluated by comparing the response spectra of the free-field motion to that of the foundation motion. Results show that changes in the response spectra are significant for heavy, stiff structures such as a reactor-containment vessel.

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

1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
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.

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

1973 ◽  
Vol 10 (03) ◽  
pp. 644-651 ◽  
Author(s):  
Peter Purdue
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Queueing Theory ◽  
Branching Process ◽  
Linear Matrix ◽  
Volterra Type ◽  
Matrix Integral ◽  
Non Linear

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.

On a stochastic integral equation of the Volterra type in telephone traffic theory

1971 ◽  
Vol 8 (02) ◽  
pp. 269-275 ◽  
Author(s):  
W. J. Padgett ◽  
C. P. Tsokos
Keyword(s):  
Integral Equation ◽  
Stochastic Integral ◽  
Random Variable ◽  
Scalar Function ◽  
List Type ◽  
Volterra Type ◽  
Stochastic Integral Equation ◽  
Image Position ◽  
Traffic Theory ◽  
Telephone Traffic

In mathematical models of phenomena occurring in the general areas of the engineering, biological, and physical sciences, random or stochastic equations appear frequently. In this paper we shall formulate a problem in telephone traffic theory which leads to a stochastic integral equation which is a special case of the Volterra type of the form where: (i) ω∊Ω, where Ω is the supporting set of the probability measure space (Ω,B,P); (ii) x(t; ω) is the unknown random variable for t ∊ R +, where R + = [0, ∞); (iii) y(t; ω) is the stochastic free term or free random variable for t ∊ R +; (iv) k(t, τ; ω) is the stochastic kernel, defined for 0 ≦ τ ≦ t < ∞; and (v) f(t, x) is a scalar function defined for t ∊ R + and x ∊ R, where R is the real line.

A volterra-type integral equation

1989 ◽  
Vol 40 (4) ◽  
pp. 438-442 ◽  
Author(s):  
S. Ashirov ◽  
Ya. D. Mamedov
Keyword(s):  
Integral Equation ◽  
Volterra Type ◽  
Type Integral
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