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1
Content available remote Existence of solutions for some nonlinear delay integrodifferential equations with nonlocal initial conditions
100%
Yan Z.
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2012
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tom Vol. 45, nr 1
67-79
EN
The main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii's fixed point theorem. An example is presented in the end to show the applications of the obtained results.
2
Content available remote Some weakly contractive mapping theorems in partially ordered spaces and applications
100%
Rhoades B. E. , Pathak H. K. , Mishra S. N.
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2012
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tom Vol. 45, nr 3
621-636
EN
The purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly (…)-contractive mappings, in a complete metric space endowed with a partial ordering. Subsequently, we apply our main results to obtain a solution of a first order periodic problem and study the possibility of optimally controlling the solutions of ordinary differential equations via dynamic programming.
3
Content available The applications of fixed-point theorem in optimisation problems
75%
Chwastek K.
Archives of Electrical Engineering
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2012
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tom Vol. 61, nr 2
189-198
EN
The fixed-point theorem is widely used in different engineering applications. The present paper focuses on its applications in optimisation. A Matlab toolbox, chich implements the branch-and-bound optimisation method based on the fixed-point theorem, is used for solving different real-life test problems, including estimation of model parameters for the Jiles-Atherton model.
4
Content available remote The boundary value problem of higher order differential equations with delay
63%
He Z. , Shen J.
Demonstratio Mathematica
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2013
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tom Vol. 46, nr 1
87--100
EN
In the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.
5
Content available Nonincreasing solutions for quadratic integral equations of Convolution type
63%
El-Sayed W. G. , Abd El-Mowla A. A. H.
Journal of Mathematics and Applications
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2019
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tom Vol. 42
95--107
EN
We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.
6
Content available The applications of fixed-point theorem in optimisation problems
44%
Chwastek K.
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