In the paper, we give necessary and sufficient conditions for a continuous on \([-\pi ,\pi ]\) function f to belong to generalized uniform Lipschitz classes defined by iterates of the Jacobi-Dunkl translation in terms of Fourier-Jacobi-Dunkl coefficients. As a corollary, we obtain analogues of Boas equivalence results and their extensions due to Tikhonov and Moricz. We extend the Jacobi-Dunkl results of Tyr and Daher obtained for moduli of smoothness of even order and introduce a new type of modulus of smoothness of odd order for a similar study. Also, we prove sufficient conditions for generalized absolute convergence of Fourier-Jacobi-Dunkl series and show their sharpness in the important \(L^2\) case using a new variant of the inverse approximation theorem.
