• Korean Journal of Mathematics
• /
• 제29권2호
• /
• pp.293-304
• /
• 2021

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Rogosinski's lemma, Subordination principle and Jack's lemma were used.

• 대한수학회보
• /
• 제50권6호
• /
• pp.2053-2059
• /
• 2013

In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권3호
• /
• pp.235-246
• /
• 2021

In this study, a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions, is considered.The results of Rogosinskis lemma and Jacks lemma have been utilized to derive novel inequalities. Also, these inequalities have been strengthened by considering the critical points which are different from zero.

• 대한수학회보
• /
• 제49권2호
• /
• pp.417-422
• /
• 2012

In this paper, we prove an analog of the generalized Schwarz lemma for meromorphic functions. Our results improve the classical generalized Schwarz lemma.

• Korean Journal of Mathematics
• /
• 제27권4호
• /
• pp.1027-1041
• /
• 2019

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the results of Jack's lemma and Hankel determinant were used. We will get a sharp upper bound for Hankel determinant H₂(1). Also, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 대한수학회논문집
• /
• 제29권1호
• /
• pp.75-81
• /
• 2014

In this paper, a boundary version of the Schwarz and Carath$\acute{e}$odory inequality are investigated. New inequalities of the Carath$\acute{e}$odory's inequality and Schwarz lemma at boundary are obtained by taking into account zeros of f(z) function which are different from zero. The sharpness of these inequalities is also proved.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제27권4호
• /
• pp.157-169
• /
• 2020

In this paper, we improve a new boundary Schwarz lemma, for analytic functions in the unit disk. For new inequalities, the results of Rogosinski's lemma, Subordinate principle and Jack's lemma were used. Moreover, in a class of analytic functions on the unit disc, assuming the existence of angular limit on the boundary point, the estimations below of the modulus of angular derivative have been obtained.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.61-72
• /
• 2016

In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권3호
• /
• pp.275-284
• /
• 2011

In this note we study the Schwarz lemma and its various versions. We find a condition for a holomorphic map to have fixed points only on the boundary of the unit disc and compare its derivatives at fixed points to get some relations among them.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제21권3호
• /
• pp.219-227
• /
• 2014

In this note we study the Schwarz lemma and inequalities for some holomorphic functions on the unit disc. Also, we obtain the inequality of the derivative of holomorphic maps at a boundary point of the unit disc and find a holomorphic map to satisfy the equality.