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1
Content available remote Ulam-Hyers stability of a parabolic partial differential equation
Marian Daniela, Ciplea Sorina Anamaria, Lungu Nicolaie
Demonstratio Mathematica
|
2019
|
Vol. 52, nr 1
475--481
EN
The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.
2
Content available An application of the Choquet theorem to the study of randomly-superinvariant measures
Rajba T.
Opuscula Mathematica
|
2012
|
Vol. 32, no. 2
317-326
EN
Given a real valued random variable Θ we consider Borel measures μ on Β (R), which satisfy the inequality μ(B) ≥ Eμ (B-Θ) (B ∈ Β (R)) or the integral inequality [formula].We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.
3
Content available remote Integral equation arising in the theory of partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
|
2010
|
Nr 43
115-126
EN
The aim of the present paper is to study some basic qualitative properties of solutions of a certain integral equation arising in the theory of partial differential equations. The well known Banach fixed point theorem and the new integral inequality with explicit estimate obtained in the present paper are used to establish the results.
4
Content available remote Approximate solutions of a certain second order integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2010
|
Nr 45
99-109
EN
The main aim of this paper is to study the approximate solutions of a certain second order Volterra type integrodifferential equation with given initial values. A variant of a certain basic integral inequality with explicit estimate is used to establish the results.
5
Content available remote On integrated Volterra integrodifferential equation of higher order
Pachpatte B. G.
Fasciculi Mathematici
|
2008
|
Nr 39
47-61
EN
In this paper we study the existence and other properties of solutions of a certain iterated Volterra integrodifferential equation of higher order. The tools employed in the analysis are based on application of the Leray-Schauder alternative and a certain integral inequality which provides explicit bound on the unknown function.
6
Content available remote Of neutral type hyperbolic integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2008
|
Nr 40
57-69
EN
In this paper we study the existence, uniqueness and other properties of solutions of a certain neutral type hyperbolic integrodifferential equation in two independent variables. The Banach fixed point theorem and a certain integral inequality with explicit estimate are used to establish the results.
7
Content available remote On higher order Volterra-Fredholm integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
|
2007
|
Nr 37
35-48
EN
In the present paper we study the existence, uniqueness and other properties of soltions of a certain higher order Volterra-Fredholm integrodifferential equation. The well known Banach fixed point theorem coupled with Bilecki type norm and the new integral inequality with explicit estimate are used to establish the results.
8
Content available remote Integral inequalities on infinite intervals
Barnett N., Dragomir S.
Demonstratio Mathematica
|
2006
|
Vol. 39, nr 3
507-514
EN
Inequalities concerning the distance between a function and some integrals on infinite intervals are given.
9
Content available remote On the existence of global solutions of evolution equations
Medved M.
Demonstratio Mathematica
|
2004
|
Vol. 37, nr 4
871--882
EN
In this paper a sufficient condition for the existence of global solutions of evolution equations is proved. In the proof a modification of the Bihari type integral inequality to the case of a weakly singular nonlinear integral inequality is used. An application to a reaction-diffusion problem is given.
10
Content available remote Qualitative behaviour of an integral equation related to some epidemic model
Brestovanská E.
Demonstratio Mathematica
|
2003
|
Vol. 36, nr 3
603--609
EN
Sufficient conditions for the uniqueness, global existence and for the convergence to zero when t -> oo of solutions of an integral equation related to an epidemic model are proved. The existence result is proved by applying the Banach fixed point theorem and for the proof of the convergence result a new type of integral inequality is used.
11
Content available remote Integral inequalities associated with inequalities of Opial type
Florkiewicz B., Kuchta M.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2002
|
Vol. 50, no 1
41-45
EN
We derive some new integral inequalities of the form: [...], h [belongs to] H, where I = (alpha, beta), -[infinity is less than or equal alpha < beta is less than or equal infinity], p > 0, H is a wide class of absolutely continuous functions h defined on I and satisfying the limit conditions h(alpha) = 0 or h(beta) = 0, the functions r, s and u are any set of functions related by the appropriate weight functions. To get the desired inequality, at first we derive an integral inequality of Opial type using a uniform method of obtaining integral inequalities with weight functions involving the function and its derivative [2].
12
Content available remote Integral inequalities of Wirtinger and Opial type in three independent variables
Pachpatte B. G.
Fasciculi Mathematici
|
1999
|
Nr 30
113-129
EN
In the present paper we establish some new Wirtinger and Opial type integral inequalities involving functions of three independent variables and their partial derivatives. The method used in the proof is elementary and our results provide new estimates on inequalities ofthis type.
13
Content available remote On some further Wirtinger-Beesack integral inequalities
Florkiewicz B., Wojteczek K.
Demonstratio Mathematica
|
1999
|
Vol. 32, nr 3
495-502
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