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Existence, uniqueness and estimates of classical solutions to some evolutionary system

Sapa L.

Opuscula Mathematica

2015

Vol. 35, no. 6

935--956

The theorem of the local existence, uniqueness and estimates of solutions in Hölder spaces for some nonlinear differential evolutionary system with initial conditions is formulated and proved. This system is composed of one partial hyperbolic second-order equation and an ordinary subsystem with a parameter. In the proof of the theorem we use the Banach fixed-point theorem, the Arzeli-Ascola lemma and the integral form of the differential problem.

Adapted quadratic approximation for logarithmic kernel integrals

Nadir M.

Fasciculi Mathematici

2012

Nr 49

75--85

In this work, we explain a new numerical schemes of collocation methods based on the adapted quadratic approximation of singular integral with logarithmic kernel. This approximation leads to obtain the numerical solution of singular integral equations with logarithmic kernel on an oriented smooth contour.

Some remarks of Borel type means of trigonometric Fourier series

Tomczak K.

Fasciculi Mathematici

2004

Nr 34

121-128

In this note we consider certain means Bi (f) of Borel type of trigonometric Fourier series of function f belonging to the Hölder space formula We give theorem on the degree of approximation of .