Vilenkin–Lebesgue points and summations of bounded multi-dimensional Vilenkin–Fourier series

In 2017, Weisz introduced the concept of ω ω -Walsh–Lebesgue points and proved that the Fejér means σ ₙ (f) σ n ( f ) of the Walsh–Fourier series of a d -dimensional integrable function f converge to the function at each ω ω -Walsh–Lebesgue point, provided that n → ∞ n → ∞ and n lies within a cone. In this paper, we aim to generalize these results to the Vilenkin–Fejér means and other summability methods of Vilenkin–Fourier series. We also present convergence theorems for θ θ -summations as well as for matrix transform and Nörlund summations.