Successive Logarithmic Coefficients of Univalent Functions

Abstract

Abstract The paper deals with logarithmic coefficients of univalent functions. The sharp lower and upper estimations of $$|\gamma _2(f)|-|\gamma _1(f)|$$ | γ 2 ( f ) | - | γ 1 ( f ) | were obtained in the class $${\mathcal {S}}$$ S , where $$\gamma _n(f)$$ γ n ( f ) denotes the n -th logarithmic coefficient of $$f\in {\mathcal {S}}$$ f ∈ S . The result is applicable to some standard subclasses of $${\mathcal {S}}$$ S . Relevant examples were indicated.