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Given a polyhedral convex function g: ℝⁿ → ℝ ∪ +∞, it is always possible to construct a family ${g ₜ}_{t > 0}$ which converges pointwise to g and such that each gₜ: ℝⁿ → ℝ is convex and infinitely often differentiable. The construction of such a family ${g ₜ}_{t > 0}$ involves the concept of cumulant transformation and a standard homogenization procedure.

Some remarks on approximation by finite element methods

Giuseppe Geymonat, Peter Oswald (1989)

Banach Center Publications

Some Remarks on Rational Müntz Approximation on [0,∞)

S. Zhou (1998)

Colloquium Mathematicae

Some spaces of entire and nuclearly entire functions on a Banach space. I.

Philip J. Boland (1974)

Journal für die reine und angewandte Mathematik

Some spaces of entire and nuclearly entire functions on a Banach space. II.

Philip J. Boland (1974)

Journal für die reine und angewandte Mathematik

Stability Theorems for Fourier Frames and Wavelet Riesz Bases.

Radu Balan (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

Nazim Mahmudov (2010)

Open Mathematics

In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.

Strong converse inequality for a spherical operator.

Lin, Shaobo, Cao, Feilong (2011)

Journal of Inequalities and Applications [electronic only]

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