Cover Image

On the jackson theorem for periodic functions in spaces with integral metric

We consider the approximation of periodic functions by trigonometric polynomials in metric (not normed) spaces that are generalizations of the spaces L p , 0 < p < 1, and L 0. In particular, we prove the multidimensional Jackson theorem in L p (T m ), 0 < p < 1.

Saved in:

Bibliographic Details
Date:	2000
Main Authors:	Pichugov, S. A., Пичугов, С. А.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2000
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/4402
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

On the Jackson theorem for periodic functions in metric spaces with integral metric. II
by: Pichugov, S. A., et al.
Published: (2011)

Inverse Jackson theorems in spaces with integral metric
by: Pichugov, S. A., et al.
Published: (2012)

Some properties of the moduli of continuity of periodic functions in metric spaces
by: Pichugov, S. A., et al.
Published: (2016)

Approximation of periodic functions by constants in the metric spaces $ϕp(L)$
by: Pichugov, S. A., et al.
Published: (1994)

Multiple modules of continuity and the best approximations of periodic functions in metric spaces
by: Pichugov, S. A., et al.
Published: (2018)

Inequalities for trigonometric polynomials in spaces with integral metric
by: Pichugov, S. A., et al.
Published: (2011)

Smoothness of functions in the metric spaces Lψ
by: Pichugov, S. A., et al.
Published: (2012)

Approximation of compressions of periodic functions in the space $L_p,\; p < 1$
by: Pichugov, S. A., et al.
Published: (1995)

Nikol’skii – Stechkin-type inequalities for the increments of trigonometric polynomials in metric spaces
by: Pichugov, S. A., et al.
Published: (2017)

Approximation of measurable periodic functions in measure by step functions
by: Pichugov, S. A., et al.
Published: (1996)

The Marchaud's inequality for multiple modules of continuity in metric spaces
by: Pichugov, S. A., et al.
Published: (2019)

On Jackson’s theorem in $L_p$ spaces
by: Tіman, M. F., et al.
Published: (1966)

Some properties of the moduli of continuity of periodic functions in metric spaces
by: S. A. Pichugov
Published: (2016)

Asymptotic behavior of the best approximations for the functions in $L_p$
by: Pichugov, S. A., et al.
Published: (1993)

On the existence of a measurable function with given values of the best approximations in $L_0$
by: Pichugov, S. A., et al.
Published: (1996)

Lower bounds for the deviations of the best linear methods of approximation of continuous functions by trigonometric polynomials
by: Pichugov, S. A., et al.
Published: (2012)

K-interpolations in problems of uniform approximation of functions
by: Pichugov , S. A., et al.
Published: (1992)

Imbedding Theorems in Metric Spaces $L_{ψ}$
by: Agoshkova, T. A., et al.
Published: (2014)

Fixed-point theorems for integral-type contractions on partial metric spaces
by: F. Sabetghadam, et al.
Published: (2016)

Fixed-point theorems for integral-type contractions on partial metric spaces
by: Altun, I., et al.
Published: (2016)

An Analog of the Jackson Inequality for Coconvex Approximation of Periodic Functions
by: Popov, P. A., et al.
Published: (2001)

Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type
by: Malyarenko, A. A., et al.
Published: (1999)

Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions
by: Agoshkova, T. A., et al.
Published: (2013)

Imbedding Theorems in Metric Spaces L_(ш)
by: T. A. Agoshkova
Published: (2014)

Second Jackson Inequality in a Sign-Preserving Approximation of Periodic Functions
by: Pleshakov, M. G., et al.
Published: (2004)

Approximation of Infinitely Differentiable Periodic Functions by Interpolation Trigonometric Polynomials in Integral Metric
by: Serdyuk, A. S., et al.
Published: (2001)

Approximation of Periodic Analytic Functions by Interpolation Trigonometric Polynomials in the Metric of the Space $L$
by: Serdyuk, A. S., et al.
Published: (2002)

Direct theorems of approximation for the functions regular in convex polygon by exponential polynomials in the integral metrics
by: Melnik, Yu. I., et al.
Published: (1988)

Inverse theorems of approximation of regular (in convex polygons) functions by exponential polynomials in the integral metric
by: Melnik , Yu. I., et al.
Published: (1988)

Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions
by: T. A. Agoshkova
Published: (2013)

Concave shells of continuity modules
by: Pichugov, S. A., et al.
Published: (2019)

Inequalities of the Jackson Type in the Approximation of Periodic Functions by Fejér, Rogosinski, and Korovkin Polynomials
by: Bozhukha, L. N., et al.
Published: (2000)

Approximation of the classes of convolutions of periodic functions by Zygmund sums in integral metrics
by: U. Z. Hrabova
Published: (2014)

Approximation of periodic functions of many variables by functions of smaller number of variables in Orlicz metric spaces
by: Babich, Yu. A., et al.
Published: (2018)

Fixed-Point Theorems and Common Fixed-Point Theorems on Spaces Equipped With Vector-Valued Metrics
by: Hosseinzadeh, H., et al.
Published: (2013)

Jackson-Type Inequalities in the Space $S^p$
by: Voitsekhivs'kyi, V. R., et al.
Published: (2003)

Kolmogorov-Type Inequalities for Periodic Functions Whose First Derivatives Have Bounded Variation
by: Babenko, V. F., et al.
Published: (2002)

Inequalities of Different Metrics for Differentiable Periodic Functions
by: Kofanov, V. A., et al.
Published: (2015)

Marshoud&#039;s inequality for multiple modules of continuity in metric spaces
by: S. A. Pichugov
Published: (2019)

Fixed-Point Theorems and Common Fixed-Point Theorems on Spaces Equipped With Vector-Valued Metrics
by: H. Hosseinzadeh, et al.
Published: (2013)