ON PRINCIPLE OF SUBORDINATION AND MAJORIZATION OF REGULAR UNIVALENTS FUNCTIONS

Abstract

The purpose of this thesis is to study the principles of subordination and majorization of regular univalent functions and try to unify those concepts of subordination and majorization by the name of quasi-subornidation. We study the sharpened form of Schwarz lemma in detail and prove that if g is subordinate to f for ｜z｜<1, then M_(p)(r, g)≤M_(p)(r, f), (0≤r<l, 0<p<∞), and obtain the coefficient bounds of f if f∈C and f∈S* After investigating MacGregor's results on majorization we introduce the concept of quasi-subordinate functions and their properties.;이 논문에서 regular univalent function의 subordination과 majorization의 성질을 공부하고 subordination과 majorization의 개념들을 quasi-subordination을 통해 관찰했다. Schwarz lemma의 sharpened form을 자세히 관찰하고 g가 f에 subordinate할 때 M_(p)(r, g)≤_(p)(r, f) (0≤r<1,0<P<∞)가 성립하고 f∈C이고 f∈S^(*)인 경우 f의 coefficient bound를 얻는다. MacGregor의 Majorization에 관한 결과를 조사한 후 quasi-subordination의 개념과 그들의 특성을 소개하였다.