scholarly journals Reduction of an Infinite System of Integral Equations of Potential Type on a One-Dimensional Lattice of Closed Curves in the Plane to a Finite System of Independent Pseudodifferential Equations on a Circle

1995 ◽  
Vol 7 (1) ◽  
pp. 37-46
Author(s):  
Valery A. Kholodnyi
Keyword(s):  
Integral Equations ◽  
Infinite System ◽  
Finite System ◽  
Closed Curves ◽  
System Of Integral Equations ◽  
Pseudodifferential Equations ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Potential Type

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

On the two-boundary first-crossing-time problem for diffusion processes

1990 ◽  
Vol 27 (01) ◽  
pp. 102-114 ◽  
Author(s):  
A. Buonocore ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Integral Equations ◽  
Diffusion Processes ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Time Problem ◽  
Crossing Time ◽  
Single Integral ◽  
First Crossing Time

The first-crossing-time problem through two time-dependent boundaries for one-dimensional diffusion processes is considered. The first-crossing p.d.f.'s from below and from above are proved to satisfy a new system of Volterra integral equations of the second kind involving two arbitrary continuous functions. By a suitable choice of such functions a system of continuous-kernel integral equations is obtained and an efficient algorithm for its solution is provided. Finally, conditions on the drift and infinitesimal variance of the diffusion process are given such that the system of integral equations reduces to a non-singular single integral equation for the first-crossing-time p.d.f.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

scholarly journals Some Coincidence and Common Fixed-Point Results on Cone b 2 -Metric Spaces over Banach Algebras with Applications to the Infinite System of Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Doaa Filali ◽  
Fahd Jarad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Banach Algebras ◽  
System Of Integral Equations ◽  
Different Types ◽  
Common Fixed Point Theorems

In this article, common fixed-point theorems for self-mappings under different types of generalized contractions in the context of the cone b 2 -metric space over the Banach algebra are discussed. The existence results obtained strengthen the ones mentioned previously in the literature. An example and an application to the infinite system of integral equations are also presented to validate the main results.

scholarly journals Solutions of an infinite system of integral equations of Volterra-Stieltjes type in the sequence spaces $\ell_{p} (1

2020 ◽  
Vol 5 (4) ◽  
pp. 3791-3808
Author(s):  
Ayub Samadi ◽  
◽  
M. Mosaee Avini ◽  
M. Mursaleen ◽  
◽  
...  
Keyword(s):  
Integral Equations ◽  
Infinite System ◽  
Sequence Spaces ◽  
System Of Integral Equations ◽  
Stieltjes Type

Heat Potentials Method in the Treatment of One-dimensional Free Boundry Problems Applied in Cryomedicine

2018 ◽  
Vol 85 (1-2) ◽  
pp. 111 ◽  
Author(s):  
Fatimat K. Kudayeva ◽  
Arslan A. Kaigermazov ◽  
Elizaveta K. Edgulova ◽  
Mariya M. Tkhabisimova ◽  
Aminat R. Bechelova
Keyword(s):  
Free Boundary ◽  
Integral Equations ◽  
Free Boundary Problems ◽  
Evolutionary Equation ◽  
Fredholm Integral Equations ◽  
Integral Expression ◽  
Boundary Problems ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Heat Potential

Free boundary problems are considered to be the most difcult and the least researched in the eld of mathematical physics. The present article is concerned with the research of the following issue: treatment of one-dimensional free boundary problems. The treated problem contains a nonlinear evolutionary equation, which occurs within the context of mathematical modeling of cryosurgery problems. In the course of the research, an integral expression has been obtained. The obtained integral expression presents a general solution to the non-homogeneous evolutionary equation which contains the functions that represent simple-layer and double-layer heat potential density. In order to determine the free boundary and the density of potential a system of nonlinear, the second kind of Fredholm integral equations was obtained within the framework of the given work. The treated problem has been reduced to the system of integral equations. In order to reduce the problem to the integral equation system, a method of heat potentials has been used. In the obtained system of integral equations instead of K(ξ; x; τ - t) in case of Dirichlet or Neumann conditions the corresponding Greens functions G(ξ; x; τ - t) or N(ξ; x; τ - t) have been applied. Herewith the integral expression contains fewer densities, but the selection of arbitrary functions is reserved. The article contains a number of results in terms of building a mathematical model of cooling and freezing processes of biological tissue, as well as their effective solution development.

scholarly journals Solvability of an infinite system of nonlinear integral equations of Volterra-Hammerstein type

2019 ◽  
Vol 9 (1) ◽  
pp. 1187-1204
Author(s):  
Agnieszka Chlebowicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Function Space ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Nonlinear Integral Equations ◽  
System Of Integral Equations ◽  
Half Axis ◽  
Suitable Measure

Abstract The purpose of the paper is to study the solvability of an infinite system of integral equations of Volterra-Hammerstein type on an unbounded interval. We show that such a system of integral equations has at least one solution in the space of functions defined, continuous and bounded on the real half-axis with values in the space l1 consisting of all real sequences whose series is absolutely convergent. To prove this result we construct a suitable measure of noncompactness in the mentioned function space and we use that measure together with a fixed point theorem of Darbo type.

On the two-boundary first-crossing-time problem for diffusion processes

1990 ◽  
Vol 27 (1) ◽  
pp. 102-114 ◽  
Author(s):  
A. Buonocore ◽  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi
Keyword(s):  
Integral Equations ◽  
Diffusion Processes ◽  
Continuous Functions ◽  
System Of Integral Equations ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Time Problem ◽  
Crossing Time ◽  
Single Integral ◽  
First Crossing Time

The first-crossing-time problem through two time-dependent boundaries for one-dimensional diffusion processes is considered. The first-crossing p.d.f.'s from below and from above are proved to satisfy a new system of Volterra integral equations of the second kind involving two arbitrary continuous functions. By a suitable choice of such functions a system of continuous-kernel integral equations is obtained and an efficient algorithm for its solution is provided. Finally, conditions on the drift and infinitesimal variance of the diffusion process are given such that the system of integral equations reduces to a non-singular single integral equation for the first-crossing-time p.d.f.

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