Inequalities for the non-tangential derivative at the boundary for holomorphic function
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In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function f(z) = z + bp+1zp+1 + bp+2zp+2 + · · · defined in the unit disc, with ℜ(f′(z)/λf′(z)+1−λ)> β, 0 ≤ β < 1, 0 ≤ λ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ξ, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.
Abstract
In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function f(z) = z + bp+1zp+1 + bp+2zp+2 + · · · defined in the unit disc, with ℜ(f′(z)/λf′(z)+1−λ)> β, 0 ≤ β < 1, 0 ≤ λ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ξ, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.
참고문헌 (9)
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