Successive coefficients of close-to-convex functions

  • 1 Lublin University of Technology, Mechanical Engineering Faculty, Lublin, Poland
Paweł ZaprawaORCID iD: https://orcid.org/0000-0002-7279-9582

Abstract

In this paper we discuss coefficient problems for functions in the class 𝒞0(k). This family is a subset of 𝒞, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate |an+1|-|an| and |an|. Moreover, it is proved that Re{an}0 for all f𝒞0(k).

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