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1
Content available Iteracje odwzorowań, orbity, twierdzenie Banacha o punkcie stałym
Ludew Jan Jakub, Różański Michał, Smoleń-Duda Barbara, Wituła Roman, Czernik Szymon
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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2021
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Nr 3
166-195
PL
Praca stanowi zbiór zadań i problemów poświęconych wprowadzeniu w teorią punktów stałych, która realizowana jest jedynie w zarysie na drugim semestrze studiów na kierunku matematyka. Stanowi niezależny byt, ale w gruncie rzeczy jest uzupełnieniem finalizowanego opracowania teoretycznego, które również zamierzamy opublikować w tym czasopiśmie.
2
Content available remote On Fractional Neutral Integro-differential Systems with State-dependent Delay in Banach Spaces
Kailasavalli S., Suganya S., Mallika Arjunan M.
Fundamenta Informaticae
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2017
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Vol. 151, nr 1/4
109--133
EN
Based on concepts for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is principally involved with existence results for fractional neutral integro-differential systems with state-dependent delay in Banach spaces. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [1]. Finally an examples are additionally offered to exhibit the achieved hypotheses.
3
Controllability of mixed Volterra–Fredholm type integrodifferential third order dispersion equations
Kumar M., Sukavanam N.
Journal of Applied Analysis
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2015
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Vol. 21, nr 1
1--7
EN
In this paper, we establish a result concerning the controllability of a mixed Volterra–Fredholm type integrodifferential third order dispersion equation. The result is obtained by using the theory of strongly continuous semigroups and the Banach fixed point theorem.
4
Content available Controllability of nonlinear stochastic systems with multiple time-varying delays in control
Karthikeyan S., Balachandran K., Sathya M.
International Journal of Applied Mathematics and Computer Science
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2015
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Vol. 25, no. 2
207--215
EN
This paper is concerned with the problem of controllability of semi-linear stochastic systems with time varying multiple delays in control in finite dimensional spaces. Sufficient conditions are established for the relative controllability of semilinear stochastic systems by using the Banach fixed point theorem. A numerical example is given to illustrate the application of the theoretical results. Some important comments are also presented on existing results for the stochastic controllability of fractional dynamical systems.
5
On a nonlinear dynamic integrodifferential equation on time scales
Pachpatte D. B.
Journal of Applied Analysis
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2010
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Vol. 16, nr 2
279-294
EN
The main objective of the present paper is to study some basic qualitative properties of solutions of a certain nonlinear integrodifferential equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain inequality with explicit estimate on time scales.
6
Content available remote The radial solution of the heat equation in the cylindrical ring
Koroński J.
Fasciculi Mathematici
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2010
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Nr 43
69-83
EN
The subject of the paper is the construction of a solution to the parabolic problem for the cylindrical ring with initial condition of Cauchy type and boundary conditions of Dirichlet type. To construct the radial solution we do not use the Bessel functions but we apply the convenient Green function, heat potentials and Banach fixed point theorem.
7
Content available remote Integral equation arising in the theory of partial differential equations
Pachpatte B. G.
Fasciculi Mathematici
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2010
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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.
8
Content available remote Of neutral type hyperbolic integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
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2008
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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.
9
Content available remote On higher order Volterra-Fredholm integrodifferential equation
Pachpatte B. G.
Fasciculi Mathematici
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2007
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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.
10
Content available remote On Volterra-Fredholm integral equation in two variables
Pachpatte B.
Demonstratio Mathematica
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2007
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Vol. 40, nr 4
839-852
EN
The aim of this paper is to study thexistence, uniqueness and other properties of solution of a certain Volterra-Fredholm integral equation in two independent variables. The main tools employed in the analysis are based on the applications of the well known Banach fixed point theorem and the new integral inequality with explicit estimate.
11
Content available remote Solution approximation of a system of integral equations by a uniformly convergent polynomials sequence
Long N. T.
Demonstratio Mathematica
|
2004
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Vol. 37, nr 1
123--132
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