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On the Difference of Coefficients of Starlike and Convex Functions

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Young Jae Sim & Derek K. Thomas, 2020. "On the Difference of Coefficients of Starlike and Convex Functions," Mathematics, MDPI, vol. 8(9), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1521-:d:409796
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