Generalized dyadic derivative and uniform convergence of its Walsh–Fourier series

Abstract. In the paper the notion of dyadic \(\lambda\)-derivative is introduced for nonnegative, nondecreasing and concave sequence \(\{\lambda_n\}^\infty_{n=0}\). Analogues of Bernstein inequality for Walsh polynomials and of inverse approximation theorem are established. Also the uniform convergence of Walsh–Fourier series to this \(\lambda\)-derivative is studied.