Analytic and Harmonic Univalent Functions

Studies on analytic univalent functions became the focus of intense researchwith theBieberbachconjectureposed in 1916 concerning the size of the moduli of the Taylor coefficients of these functions. In efforts towards its resolution, the conjecture inspired the development of several ingeniously different mathematical techniques with powerful influence. These techniques include Lowner’s parametric representation method, the area method,Grunsky inequalities, and methods of variations.Despite the fact that the conjecture was affirmatively settled by de Branges in 1985, complex function theory continued to remain a highly active relevant area of research