Towards Best Approximations for x α $$\left \vert x\right \vert ^{\alpha }$$

Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

Mathematica Slovaca ◽

10.1515/ms-2017-0314 ◽

2019 ◽

Vol 69 (6) ◽

pp. 1367-1380 ◽

Cited By ~ 2

Author(s):

Stanislav Chaichenko ◽

Andrii Shidlich ◽

Fahreddin Abdullayev

Keyword(s):

Fractional Order ◽

Moduli Of Smoothness ◽

Best Approximations ◽

Approximation Theorems ◽

Inverse Approximation ◽

Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

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Approximability of the classes $ B_{p,\theta}^r$ of periodic functions of several variables by linear methods and best approximations

Sbornik Mathematics ◽

10.1070/sm2004v195n02abeh000801 ◽

2004 ◽

Vol 195 (2) ◽

pp. 237-261 ◽

Cited By ~ 5

Author(s):

A S Romanyuk

Keyword(s):

Periodic Functions ◽

Best Approximations ◽

Several Variables

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Best approximations and fixed points of nonexpansive maps in hilbert spaces sehie park

Numerical Functional Analysis and Optimization ◽

10.1080/01630569708816783 ◽

1997 ◽

Vol 18 (5-6) ◽

pp. 447-454 ◽

Cited By ~ 1

Author(s):

Sehie Park ◽

S. p. Singh ◽

B. Watson ◽

T. E. Williamson

Keyword(s):

Fixed Points ◽

Hilbert Spaces ◽

Best Approximations ◽

Nonexpansive Maps

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On Best Approximations of Linear Operators

I. J. Schoenberg Selected Papers ◽

10.1007/978-1-4899-0433-1_20 ◽

1988 ◽

pp. 397-405

Author(s):

I. J. Schoenberg

Keyword(s):

Linear Operators ◽

Best Approximations

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The approximation problem and existence of best approximations

Approximation Theory and Methods ◽

10.1017/cbo9781139171502.002 ◽

1981 ◽

pp. 1-12

Keyword(s):

Approximation Problem ◽

Best Approximations

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On the orders of the best approximations of integrals of functions by integrals of rank σ

Nonlinear Oscillations ◽

10.1007/s11072-008-0001-0 ◽

2007 ◽

Vol 10 (4) ◽

pp. 0-0

Author(s):

A. I. Stepanets ◽

A. L. Shidlich

Keyword(s):

Best Approximations

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Im-Quasi Upward Sets, with Their Best Approximations

Numerical Functional Analysis and Optimization ◽

10.1080/01630563.2010.519135 ◽

2010 ◽

Vol 31 (11) ◽

pp. 1261-1271

Author(s):

M. Iranmanesh ◽

F. Solimany

Keyword(s):

Best Approximations

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On Best Approximations of Linear Operators

I.J. Schoenberg Selected Papers ◽

10.1007/978-1-4612-3946-8_43 ◽

1988 ◽

pp. 803-811

Author(s):

I. J. Schoenberg

Keyword(s):

Linear Operators ◽

Best Approximations

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Minimal Projections and Near-Best Approximations by Multivariate Polynomial Expansion and Interpolation

Multivariate Approximation Theory II ◽

10.1007/978-3-0348-7189-1_20 ◽

1982 ◽

pp. 241-254 ◽

Cited By ~ 2

Author(s):

John C. Mason

Keyword(s):

Polynomial Expansion ◽

Best Approximations ◽

Multivariate Polynomial ◽

Minimal Projections

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CONTINUED FRACTIONS, INTERMEDIATE FRACTIONS AND THEIR RELATION TO THE BEST APPROXIMATIONS

Journal of Science and Arts ◽

10.46939/j.sci.arts-20.3-a05 ◽

2020 ◽

Vol 20 (3) ◽

pp. 545-560

Author(s):

LUKA MILINKOVIC ◽

BRANKO MALESEVIC ◽

BOJAN BANJAC

Keyword(s):

Continued Fractions ◽

Continued Fraction ◽

Rational Approximations ◽

Best Approximations ◽

Current State ◽

The Subject ◽

State Of Art

The subject of this paper is the current state of art in theory of continued fractions, intermediate fractions and their relation to the best rational approximations of the first and second kind. The paper provides an overview of the some well known and even some new properties of continued fractions, and the various terms associated with them. In addition to intermediate fractions, paper considers the fine intermediate fractions and gave some statements to position these fractions in the continued fraction representation of numbers.

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