Degree of Approximation by the $$ \left( {T.\,E^{\,1} } \right) $$ T . E 1 Means of Conjugate Series of Fourier Series in the Hölder Metric

Abstract

We extend the results of Singh and Mahajan (Int J Math Math Sci 2008:9, 2008) which in turn generalizes the result of Lal and Yadav (Bull Cal Math Soc 93:191–196, 2001). In this paper, we determine the degree of approximation of functions $$ \widetilde{f\,} \in H_{\omega } , $$ a new Banach space using $$ \left( {T.\,E^{\,1} } \right) $$ summability means of conjugate series of Fourier series. Also, some corollaries have also been deduced from our main theorem and particular cases.