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A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn(f; t) of generalized Fourier series on a parallel hexagon domain Ω associating with three-direction partition. We prove that an operator Wn(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.