Uniform convergence of trigonometric series with $p$-bounded variation coefficients

Abstract

In the present paper we introduce a new class of sequences called $GMS\left(p, \beta ,r\right) ,$ which is the generalization of a class considered by Tikhonov in [9] and Szal in [10]. Moreover, we obtained in this note sufficient and necessary conditions for the uniform convergence of sine and cosine series with $\left(p,\beta ,r\right) -$ general monotone coefficients.