지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
이용수
초록· 키워드
오류제보하기
In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for $\left\vert f^{\prime}(0)\right\vert $ and sharp lower bounds for $\left\vert f^{\prime}(c)\right\vert $ with $c\in \partial D=\left\{ z:\left\vert z\right\vert=1\right\} $. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function $f(z) $ from below according to the second Taylor coefficients of $f$ about $z=0$ and $z=z_{0}\neq 0.$ Thanks to these inequalities, we see the relation between $\vert f^{\prime }(0)\vert$ and $\Re f(0).$ Similarly, we see the relation between $\Re f(0)$ and $\vert f^{\prime }(c)\vert$ for some $c\in\partial D.$ The sharpness of these inequalities is also proved.
목차
등록된 정보가 없습니다.
참고문헌 (15)
참고문헌 신청
T. Akyel / 2017 / Some remarks on Schwarz lemma at the boundary / Filomat 31(13):4139~4151
T. A. Azero_glu / 2013 / A re_ned Schwarz inequality on the boundary / Complex Variables and Elliptic Equations 58:571~577
H. P. Boas / 2010 / Julius and Julia: Mastering the art of the Schwarz lemma / American Mathematical Monthly 117:770~785
V. N. Dubinin / 2004 / The Schwarz inequality on the boundary for functions regular in the disc / J. Math. Sci 122:3623~3629
G. M. Golusin / 1969 / Geometric Theory of Functions of Complex Variable Translations of Mathematical Monographs / American Mathematical Society 26
T. A. Azero_glu / 2013 / A re_ned Schwarz inequality on the boundary / Complex Variables and Elliptic Equations 58:571~577
H. P. Boas / 2010 / Julius and Julia: Mastering the art of the Schwarz lemma / American Mathematical Monthly 117:770~785
V. N. Dubinin / 2004 / The Schwarz inequality on the boundary for functions regular in the disc / J. Math. Sci 122:3623~3629
G. M. Golusin / 1969 / Geometric Theory of Functions of Complex Variable Translations of Mathematical Monographs / American Mathematical Society 26
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Some results for the class of analytic functions concerned with symmetric points
한국수학논문집
2023 .03
-
Inequalities for the angular derivatives of certain classes of holomorphic functions in the unit disc
대한수학회보
2016 .01
-
Results associated with the Schwarz lemma on the boundary
대한수학회논문집
2023 .04
-
Some remarks on the Subordination Principle for analytic functions concerned with Rogosinski's lemma
한국수학논문집
2021 .01
-
Estimates for Second non-tangential derivatives at the boundary
대한수학회논문집
2017 .07
-
AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY
순수 및 응용수학
2016 .01
-
A SHARP SCHWARZ LEMMA AT THE BOUNDARY
순수 및 응용수학
2015 .01
-
Applications of the Schwarz Lemma and Jack’s Lemma for the Holomorphic Functions
Kyungpook Mathematical Journal
2020 .01
-
Applications of Jack's lemma for certain subclasses of holomorphic functions on the unit disc
대한수학회논문집
2019 .01
-
Some results concerned with Hankel determinant for $\mathcal{N}\left( \mathcal{\alpha }\right)$ class
대한수학회논문집
2021 .10
-
CARATHÉODORY'S INEQUALITY ON THE BOUNDARY
순수 및 응용수학
2015 .01
-
Estimates for a Certain Subclass of Holomorphic Functions
순수 및 응용수학
2019 .01
-
Bounds of Hankel determinants for analytic function
한국수학논문집
2020 .01
-
Erratum : A new iteration method for fixed point of nonexpansive mapping in uniformly convex Banach space
한국수학논문집
2023 .03
-
INEQUALITIES CONCERNING THE POLAR DERIVATIVES OF POLYNOMIALS WITH RESTRICTED ZEROS
Nonlinear Functional Analysis and Applications
2019 .01
-
BEHAVIOR OF HOLOMORPHIC FUNCTIONS ON THE BOUNDARY OF THE UNIT DISC
순수 및 응용수학
2017 .08
-
A sharp Carath\'{e}odory's inequality on the boundary
대한수학회논문집
2016 .01
-
HOPF'S BOUNDARY TYPE BEHAVIOR FOR AN INTERFACE PROBLEM
대한수학회지
2017 .01
-
Some remarks for $\lambda$-spirallike function of complex order at the boundary of the unit disc
대한수학회논문집
2021 .10
-
Applications of the Jack's Lemma for Analytic Functions concerned with Rogosinski's Lemma
순수 및 응용수학
2021 .08
이 논문의 저자 정보
최근 본 자료
댓글(0)
0