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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
The successive approximations method and error estimation in terms of at most the first derivative for delay ordinary differential equations
Author(s):
Alexandru Mihai Bica
Department of Mathematics,
University of Oradea,
Str. Armatei Romane no.5,
410087, Oradea,
Romania
smbica@yahoo.com
abica@uoradea.ro
Abstract:
We present here a numerical method for first order delay ordinary differential
equations, which use the Banach's fixed point theorem, the sequence of
successive approximations and the trapezoidal quadrature rule. The error
estimation of the method uses a recent result of P. Cerone and S.S. Dragomir
about the remainder of the trapezoidal quadrature rule for Lipchitzian
functions and for functions with continuous first derivative.
Paper's Title:
Good and Special Weakly Picard Operators for the Stancu Operators with Modified Coefficients
Author(s):
Loredana-Florentina Galea and Alexandru-Mihai Bica
The Agora University of Oradea,
Piata Tineretului no. 8,
410526, Oradea,
Romania
University of Oradea,
Str. Universitatii No. 1,
410087, Oradea,
Romania
loredana.galea@univagora.ro
smbica@yahoo.com
abica@uoradea.ro
Abstract:
In this paper some properties of good and special weakly Picard operators for the Stancu operators with modified coefficients are obtained. In the study of the sequence of iterates of these operators, we obtain the property of dual monotone iteration.
Paper's Title:
Parameter dependence of the solution of second order nonlinear ODE's via Perov's fixed point theorem
Author(s):
A. M. Bica, S. Muresan and G. Grebenisan
University of Oradea,
Str. Armatei Romane no.5, 410087,
Oradea, Romania.
smbica@yahoo.com
smuresan@uoradea.ro
grebe@uoradea.ro
Abstract:
Using the Perov's fixed point theorem, the smooth dependence by parameter of
the solution of a two point boundary value problem corresponding to nonlinear
second order ODE's is obtained.
Paper's Title:
Traub-Potra-Type Method for Set-Valued Maps
Author(s):
Ioannis K. Argyros and Saïd Hilout
Cameron University,
Department of Mathematics Sciences,
Lawton, OK 73505,
USA
URL: http://www.cameron.edu/~ioannisa/
Poitiers University,
Laboratoire de Mathematiques et Applications,
Bd. Pierre et Marie Curie, Teleport 2, B.P. 30179,
86962 Futuroscope Chasseneuil Cedex,
France
said.hilout@math.univ-poitiers.fr
http://www-math.univ-poitiers.fr/~hilout/
Abstract:
We introduce a new iterative method for approximating a locally unique solution of variational inclusions in Banach spaces by using generalized divided differences of the first order. This method extends a method considered by Traub (in the scalar case) and by Potra (in the Banach spaces case) for solving nonlinear equations to variational inclusions. An existence-convergence theorem and a radius of convergence are given under some conditions on divided differences operator and Lipschitz-like continuity property of set-valued mappings. The R-order of the method is equal to the unique positive root of a certain cubic equation, which is $1.839..., and as such it compares favorably to related methods such as the Secant method which is only of order $1.618....
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