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In this paper, we review the works of the authors ([10], [23]) etc. and establish two theorems on degree of convergence of a function g and conjugate of a function ˜g in generalized Zygmund (Z(λ) r , r ≥ 1) space using Hausdorff-Matrix (∧T) operator of its Fourier series and conjugate Fourier series respectively based on the findings of the review. Our results generalize several earlier results. Some important corollaries are also deduced from our main theorems.