Rate of Convergence of Certain Fourier Series of Functions of Generalized Bounded Variation

In this paper, we discuss the rate of convergence of the rational Fourier series and conjugate rational Fourier series of functions of generalized bounded variation. In particular, well-known Wiener’s theorem and Siddiqi’s theorem for functions of $$p$$ -bounded variation are proved in more general complete rational orthogonal system and also results proved for wider class than the class functions of bounded variation and of p- $$\{ {{n}^{\alpha }}\} $$ -bounded variation.