(untitled) (Communications in Mathematical Research, 2021)
A new Rogosinski-type kernel function is constructed using kernel function of partial sums S_n(f;t) of generalized Fourier series on a parallel hexagon domain Ω associating with three-direction partition. We prove that an operator W_n(f;t) with the new kernel function converges uniformly to any continuous function f(t) ∈ C_∗(Ω) (the space of all continuous functions with period Ω) on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.