Neutrosophic and Information Fusion NIF 2836-7863 10.54216/NIF https://www.americaspg.com/journals/show/3208 2023 2023 Cape Peninsula University of Technology, Faculty of Applied Science, South Africa Agnes Agnes In this research, we study the problem of determining the degree of approximation of functions using the Hausdorff method, and we can do this by proving the following results: If f∈Lip(α,p)with α>1p and  be a continues aimost everywhere and 2m periodic function,Then the degree of approximation of (f ) ̃using hausdorff means of conjugate fourier series, is given by: 〗|(|H ̃_((n+λ) )  (f,a)-(f ) ̃(a)|)|_p=0((n+λ)^(1p-α)  ) If  f be a 2m periodic function, continues almost everywhere on [–m,m]  andbelonging to the class Z_(α,p ),p≥1 .then the degree of approximation of function f of fouier series using hausdorff means,is given by: E_((n+λ) ) (f)= inf_((n+λ) ) ‖H_((n+λ) )-f‖_(α,p)=0(1((n+λ) ) ∫_(1(n+λ))^m▒〖t^(α-2)v(t)  dt〗)  (5) where〖  t〗^αand v the zygmund moduli of continuity sunch that  t^αv(t) positive and monotonic function.   2024 2024 01 08 10.54216/NIF.040201 https://www.americaspg.com/articleinfo/39/show/3208