Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2013
Volume
Vol. 33
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 33 (2013)
Projects
Pages
Articles
Fractional order Riemann-Liouville integral inclusions with two independent variables and multiple delay
(2013) Abbas, Saïd; Benchohra, Mouffak
In the present paper we investigate the existence of solutions for a system of integral inclusions of fractional order with multiple delay. Our results are obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case.
Some generalized method for constructing nonseparable compactly supported wavelets in L2(R2)
(2013) Banaś, Wojciech
In this paper we show the construction of nonseparable compactly supported bi-variate wavelets. We deal with the dilation matrix $A = \tiny{\left[\begin{matrix}0 & 2 \cr 1 & 0 \cr \end{matrix} \right]}$ and some three-row coefficient mask, that is a scaling function that satisfies a dilation equation with scaling coefficients which can be contained in the set $\{c_{n}\}_{n \in\mathcal{S}},$ where $\mathcal{S}=S_{1} \times \{0,1,2\},$ $S_{1} \subset \mathbb{N},$ $\sharp S_{1} \lt \infty.$
Existence of solution of sub-elliptic equations on the Heisenberg group with critical growth and double singularities
(2013) Chen, Jianqing; Rocha, Eugénio M.
For a class of sub-elliptic equations on Heisenberg group $\mathbb{H}^N$ with Hardy type singularity and critical nonlinear growth, we prove the existence of least energy solutions by developing new techniques based on the Nehari constraint. This result extends previous works, e.g., by Han et al. [Hardy-Sobolev type inequalities on the H-type group, Manuscripta Math. 118 (2005), 235–252].
Stability by Krasnoselskii's theorem in totally nonlinear neutral differential equations
(2013) Derrardjia, Ishak; Ardjouni, Abdelouaheb; Djoudi, Ahcene
In this paper we use fixed point methods to prove asymptotic stability results of the zero solution of a class of totally nonlinear neutral differential equations with functional delay. The study concerns $x'(t)=a(t)x^3(t)+c(t)x'(t-r(t))+b(t)x^3(t-r(t)).$ The equation has proved very challenging in the theory of Liapunov's direct method. The stability results are obtained by means of Krasnoselskii-Burton's theorem and they improve on the work of T.A. Burton (see Theorem 4 in [Liapunov functionals, fixed points, and stability by Krasnoselskii's theorem, Nonlinear Studies 9 (2001), 181-190]) in which he takes $c=0$ in the above equation.
A unified representation of some starlike and convex harmonic functions with negative coefficients
(2013) El-Ashwah, Rabha Mohammad Mostafa; Aouf, M. K.; Hassan, A. A. M.; Hassan, A. H.
In this paper we introduce a unified representation of starlike and convex harmonic functions with negative coefficients, related to uniformly starlike and uniformly convex analytic functions. We obtain extreme points, distortion bounds, convolution conditions and convex combinations for this family.