Approximation on the spherical cap is different from that on the sphere which requires us to construct new operators. This paper discusses the approximation on the spherical cap. That is, so called Jackson-type operator {J_k,s^m}_k=1^∞ is constructed to approximate the function defined on the spherical cap D(x_0,γ). We thus establish the direct and inverse inequalities and obtain saturation theorems for {J_k,s^m}_k=1^∞ on the cap D(x_0,γ). Using methods of K-functional and multiplier, we obtain

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... the inequality C_1 J_k,s^m(f)-f_D,p≤ω^2(f, k^-1)_D,p≤ C_2 _v≥ k J_v,s^m(f) - f_D,p and that the saturation order of these operators is O(k^-2), where ω^2(f, t)_D,p is the modulus of smoothness of degree 2, the constants C_1 and C_2 are independent of k and f.