Successive coefficients of convex functions
Derek Thomas

TL;DR
This paper establishes sharp bounds on the differences of successive coefficients for convex functions analytic in the unit disk, contributing to the understanding of coefficient behavior in geometric function theory.
Contribution
It provides the first sharp bounds on the differences of successive coefficients for convex functions, specifically for |a_3| - |a_2| and |a_4| - |a_3|.
Findings
|a_3| - |a_2| 25/48
|a_4| - |a_3| 25/48
Both inequalities are proven to be sharp.
Abstract
It is shown that for analytic and convex in and given by , the difference of coefficients and . Both inequalities are sharp.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic and geometric function theory · Functional Equations Stability Results · Mathematical Inequalities and Applications
