A random integral equation of the volterra type

Author(s):  
Chris P. Tsokos ◽  
W. J. Padgett
2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain

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.


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

1972 ◽  
Vol 62 (2) ◽  
pp. 453-470
Author(s):  
R. J. Scavuzzo ◽  
D. D. Raftopoulos ◽  
J. L. Bailey

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.


1988 ◽  
Vol 25 (02) ◽  
pp. 257-267 ◽  
Author(s):  
D. Szynal ◽  
S. Wedrychowicz

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.


1973 ◽  
Vol 10 (03) ◽  
pp. 644-651 ◽  
Author(s):  
Peter Purdue

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.


1971 ◽  
Vol 8 (02) ◽  
pp. 269-275 ◽  
Author(s):  
W. J. Padgett ◽  
C. P. Tsokos

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.


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

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