Approximation of Functions of the Classes <inline-formula><math display="inline"><semantics><mrow><msubsup><mi mathvariant="bold-italic">C</mi><mrow><mi mathvariant="bold-italic">β</mi></mrow><mi mathvariant="bold-italic">ψ</mi></msubsup><msup><mi mathvariant="bold-italic">H</mi><mi mathvariant="bold-italic">α</mi></msup></mrow></semantics></math></inline-formula> by Linear Methods Summation of Their Fourier Series

Abstract

In this paper, we considered arbitrary linear summation methods of Fourier series specified by a set of continuous functions dependent on the real parameter and established their approximation properties. We obtained asymptotic formulas for the exact upper bounds of the deviations of operators generated by λ-methods of Fourier series summation from the functions of the classes CβψHα under certain restrictions on the functions ψ.

Keywords

• classes of (<i>ψ</i>,<i>β</i>)-differentiable functions
• Fourier series
• λ-methods summation
• asymptotic equality
• uniform metric