On the Difference of Coefficients of Starlike and Convex Functions

Young Jae Sim and Derek K. Thomas
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Young Jae Sim: Department of Mathematics, Kyungsung University, Busan 48434, Korea
Derek K. Thomas: Department of Mathematics, Swansea University, Bay Campus, Swansea SA1 8EN, UK

Mathematics, 2020, vol. 8, issue 9, 1-11

Abstract: Let f be analytic in the unit disk D = { z ∈ C : | z | < 1 } , and S be the subclass of normalized univalent functions given by f ( z ) = z + ∑ n = 2 ∞ a n z n for z ∈ D . Let S * ⊂ S be the subset of starlike functions in D and C ⊂ S the subset of convex functions in D . We give sharp upper and lower bounds for | a 3 | − | a 2 | for some important subclasses of S * and C .

Keywords: univalent function; starlike function; convex function; difference of coefficients (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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