ON STRONG APPROXIMATION IN GENERALIZED HOLDER AND ZYGMUND SPACES

TThe 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 Holder and Zygmund spaces. To elaborate its use, we deduce some corollaries and a discussion follows the results.