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Abstract: In the present paper, a new theorem on the degree of approximation of function conjugate to a 2π periodic function f belonging to the generalized weighted Lipschitz -class by dropping the monotonicity condition on the generating sequence {pn } has been established which in turn generalizes the results of Lal (2009) [12] on Fourier series. We also note some errors appearing in the paper of Lal (2009) [12] and rectify them in the view of observations of Rhoades et al. (2011) [22]. [Copyright &y& Elsevier]

Abstract: In a recent paper Lal and Yadov obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions. [Copyright &y& Elsevier]

Recently, L.N. Mishra et al. obtained a new theorem on the degree of approximation of function f ̃ : conjugate to a 2 π periodic function f belonging to the generalized weighted Lipschitz W ( L r , ξ ( t ) ) ( r ⩾ 1 ) -class (Mishra et al., 2014). In this note, we point out that the conclusion of the theorem only holds for the constant functions, and thus the result is trivial. [ABSTRACT FROM AUTHOR]