On Strong Approximation in Generalized Hölder and Zygmund Spaces

Abstract

The strong approximation of a function is a useful tool to analyze the convergence of its Fourier series. It is based on the summability techniques. However, unlike matrix summability methods, it uses non-linear methods to derive an auxiliary sequence using approximation errors generated by the series under analysis. In this paper, we give some direct results on the strong means of Fourier series of functions in generalized Hölder and Zygmund spaces. To elaborate its use, we deduce some corollaries.

Keywords

• approximation
• strong means
• summability
• Hölder
• Zygmund