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1
Content available remote Convergence of generalized sampling series in weighted spaces
Acar Tuncer, Alagöz Osman, Aral Ali, Costarelli Danilo, Turgay Metin, Vinti Gianluca
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
153--162
EN
The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.
2
Content available remote Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators
Mursaleen M., Nasiruzzaman M., Wafi A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
175--189
EN
In this paper, we introduce the q-analogue of the Jakimovski-Leviatan type modied operators introduced by Atakut with the help of the q-Appell polynomials. We obtain some approximation results via the well-known Korovkin’s theorem for these operators. We also study convergence properties by using the modulus of continuity and the rate of convergence of the operators for functions belonging to the Lipschitz class. Moreover, we study the rate of convergence in terms of modulus of continuity of these operators in a weighted space.
3
Content available remote Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies
Chinchaladze N., Jaiani G.
Archives of Mechanics
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2017
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Vol. 69, nr 4-5
305--316
EN
Antiplane strain (shear) of orthotropic non-homogeneous prismatic shell-like bodies are considered when the shear modulus depending on the body projection (i.e., on a domain lying in the plane of interest) variables may vanish either on a part or on the entire boundary of the projection. We study the dependence of the well-posedness of the boundary conditions (BCs) on the character of the vanishing of the shear modulus. The case of vibration is considered as well.
4
Content available remote A regularity criterion for positive part of radial component in the case of axially symmetric Navier-Stokes equations
Kubica A.
Demonstratio Mathematica
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2015
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Vol. 48, nr 1
62--72
EN
We examine the conditional regularity of the solutions of Navier–Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of velocity satisfies a weighted Serrin type condition and in addition angular component satisfies some condition, then the solution is regular.
5
Content available remote Harmonic vibration of cusped plates in the N-th approximation of Vekua’s hierarchical models
Chinchaladze N.
Archives of Mechanics
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2013
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Vol. 65, nr 5
345--365
EN
In this paper elastic cusped symmetric prismatic shells (i.e., plates of variable thickness with cusped edges) in the N-th approximation of Vekua’s hierarchical models are considered. The well-posedness of the boundary value problems (BVPs) under the reasonable boundary conditions at the cusped edge and given displacements at the non-cusped edge is studied in the case of harmonic vibration. The classical and weak setting of the BVPs in the case of the N-th approximation of hierarchical models is considered. Appropriate weighted functional spaces are introduced. Uniqueness and existence results for the variational problem are proved. The structure of the constructed weighted space is described and its connection with weighted Sobolev spaces is established.
6
Content available remote On weighted harmonic Bergman spaces
Petrosyan A.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
73-83
EN
This paper is devoted to the investigation of the weighted Bergman harmonic spaces bp/alpha(B] in the unit ball in Rn. The reproducing kernel Ralpha for the ball is constructed and the integral representation for functions in bp/alpha(B) by means of this kernel is obtained. Besides an linear mapping between the bp/alpha(B) spaces and the ordinary L2-space on the unit sphere, which has an explicit form of integral operator along with its inversion, is established.
7
Content available remote Two-weighted norm inequalities for the fractional integral operator between L^p and Lipschitz spaces
Pradolini G.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2001
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[Z] 41
147-169
EN
We characterize the pairs of weights for which the fractional integral of order y, I_y, is bounded from weighted Lebesgue spaces L^ into suitable weighted BMO and Lipschitz integral spaces with a weight w. We also study the properties of the classes of weights that arise in connection with this boundedness of I-y.
8
Content available remote On integral equation in space-time
Hącia L.
Demonstratio Mathematica
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1999
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Vol. 32, nr 4
795-805
EN
Integral equations in space-time play very important role in wave and heat conduction theory. Particular cases of these equations of so-called mixed integral equations or Volterra-Fredholm integral equations arise in the mathematical modelling of the spatio-temporal development of an epidemic. Some initial-boundary problems for a number of differential partial equations in physics, mechanics and technology are reducible to the considered integral equations. In this paper some methods for solving these linear integral equations are presented in weighted spaces. It is shown that better results can be obtained in weighted spaces.
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