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Approximation by q-analogue of modified Jakimovski-Leviatan-Stancu type operators

Mursaleen M., Nasiruzzaman M., Wafi A.

Demonstratio Mathematica

2017

Vol. 50, nr 1

175--189

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.

On the dependence of parameters in the equivalence theorem for the real method

Cobos F., Fernández-Cabrera L. M., Karadzhov G. E., Kühn T.

Commentationes Mathematicae

2015

Vol 55, No. 2

79--87

We determine the exact dependence on θ,q,p of the constants in the equivalence theorem for the real interpolation method (A0,A1)θ,q with pairs of p-normed spaces.

Quantitative estimates for the Lupas q-analogue of the Bernstein operator

Finta Z.

Demonstratio Mathematica

2011

Vol. 44, nr 1

123-130

We establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupas in 1987 and for the approximation properties of the limit Lupas operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems.

Real Interpolation between Row and Column Spaces

Pisier G.

Bulletin of the Polish Academy of Sciences. Mathematics

2011

Vol. 59, no 3

237--259

We give an equivalent expression for the K-functional associated to the pair of operator spaces (R,C) formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair (Mn(R),Mn(C)) (uniformly over n). More generally, the same result is valid when Mn (or B(ℓ2)) is replaced by any semi-finite von Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust-Piquard) that is valid for the Lorentz spaces Lp,q(τ) associated to a non-commutative measure τ, simultaneously for the whole range 1≤p,q<∞, regardless of whether p<2 or p>2. Actually, the main novelty is the case p=2, q/=2. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert–Schmidt norm.