본문 바로가기
KERD
논문KCI 등재

THE TILTED CARATHEODORY CLASS AND ITS APPLICATIONS

Li-Mei Wang
대한수학회 (The Korean Mathematical Society)|2012.07|대한수학회지 (Journal of the KMS)|제49권 제4호|pp. 671-686|DOI http://dx.doi.org/

1

조회

0

다운로드

2

인용

0

참고문헌

키워드

convolutionsubordination.the tilted Caratheodory classλ-spirallike functionsclose-to-convex functions with argument λ
주제분류수학

초록

This paper mainly deals with the tilted Caratheodory class by angle λ 2 (-π/2,π /2) (denoted by Pλ) an element of which maps the unit disc into the tilted right half-plane {w : Re eiλw > 0}. Firstly we will characterize Pλ from different aspects, for example by subordi-nation and convolution. Then various estimates of functionals over Pλare deduced by considering these over the extreme points of Pλ or the knowledge of functional analysis. Finally some subsets of analytic func-tions related to P including close-to-convex functions with argument λ,-spirallike functions and analytic functions whose derivative is in Pλ are also considered as applications.

Abstract

This paper mainly deals with the tilted Caratheodory class by angle λ 2 (-π/2,π /2) (denoted by Pλ) an element of which maps the unit disc into the tilted right half-plane {w : Re eiλw > 0}. Firstly we will characterize Pλ from different aspects, for example by subordi-nation and convolution. Then various estimates of functionals over Pλare deduced by considering these over the extreme points of Pλ or the knowledge of functional analysis. Finally some subsets of analytic func-tions related to P including close-to-convex functions with argument λ,-spirallike functions and analytic functions whose derivative is in Pλ are also considered as applications.

참고문헌 (30)

  1. O. P. Ahuja, "A survey on spiral-like and related function classes", Math. Chronicle, 20, pp.39~66 (1991)
  2. S. D. Bernardi, "New distortion theorems for functions of positive real part and appli- cations to the partial sums of univalent convex functions", Proc. Amer. Math. Soc, 45, pp.113~118 (1974)
  3. P. L. Duren, "Univalent Functions, Grundlehren Math. Wiss. 259" (1983), Springer-Verlag
  4. S. Gelfer, "On the class of regular functions which do not take on any pair of values and -w", Mat. Sb, 19, pp.33~46 (1946)
  5. A. W. Goodman, "Univalent Functions. Vol. II" (1983), Mariner Publishing Co. Inc
  6. I. Graham, "Geometric Function Theory in One and Higher Dimensions" (2003), Marcel Dekker, Inc
  7. F. Gray, "Functions whose derivatives take values in a half-plane", Proc. Amer. Math. Soc, 104(1), pp.215~218 (1988)
  8. D. J. Hallenbeck, "Linear Problems and Convexity Techniques in Geometric Function Theory, Monographs and Studies in Mathematics" (1984), Pitman
  9. G. Herglotz, "Uber Potenzreihen mit positivem, reellen Teil in Einheitskreis", Ber. Verh. Sachs. Akad. Wiss. Leipzig, pp.501~511 (1911)
  10. F. Holland, "The extreme points of a class of functions with positive real part", Math. Ann, 202, pp.85~87 (1973)
  11. Y. C. Kim, "Growth and coefficient estimates for uniformly locally uni- valent functions on the unit disk", Rocky Mountain J. Math, 32(1), pp.179~200 (2002)
  12. T. Sugawa, "A conformal invariant for nonvanishing analytic functions and its applications", MICHIGAN MATHEMATICAL JOURNAL, 54 (2006), MICHIGAN MATHEMATICAL JOURNAL
  13. T. Sugawa, "Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions", PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 49(1) (2006), CAMBRIDGE UNIV PRESS
  14. Y. C. Kim, "A note on Bazilevific functions", Taiwanese J. Math, 13(5), pp.1489~1495 (2009)
  15. R. A. Kortram, "The extreme points of a class of functions with positive real part", Bull. Belg. Math. Soc. Simon Stevin, 4(4), pp.449~459 (1997)
  16. R. J. Libera, "Some radius of convexity problems", Duke Math. J, 31, pp.143~158 (1964)
  17. T. H. MacGregor, "Functions whose derivative has a positive real part", Trans. Amer. Math. Soc, 104, pp.532~537 (1962)
  18. M. Nunokawa, "On the univalency and multivalency of certain analysis functions", Math. Z, 104, pp.394~404 (1968)
  19. M. S. Robertson, "Variational methods for functions with positive real part", Trans. Amer. Math. Soc, 102, pp.82~93 (1962)
  20. M. S. Robertson, "Extremal problems for analytic functions with positive real part and applica- tions", Trans. Amer. Math. Soc, 106, pp.236~253 (1963)
  21. M. S. Robertson, "Radii of star-likeness and close-to-covexity", Proc. Amer. Math. Soc, 16, pp.847~852 (1965)
  22. St. Ruscheweyh, "Convolution in geometric function theory", Sem. Math. Sup, 83 (1982), University of Montreal
  23. St. Ruscheweyh, "On certain extremal problems for functions with positive real part", Proc. Amer. Math. Soc, 61(2), pp.329~334 (1976)
  24. K. Sakaguchi, "A variational method for functions with positive real part", J. Math. Soc. Japan, 16, pp.287~297 (1964)
  25. I. Schur, "Uber Potenzreihen, die im Innern des Einheitskreises beschrankt sind", J. Reine Angew. Math, 147, pp.205~232 (1918)
  26. L. Spacek, "Contribution a la theorie des fonctions univalentes", Casopis Pest. Mat.-Fys, 62, pp.12~19 (1932)
  27. L.-M. Wang, "Coefficient estimates for close-to-convex functions with argument", Bull. Berg. Math. Soc
  28. S. Yamashita, "Gel'fer functions, integral means, bounded mean oscillation, and univa- lency", Trans. Amer. Math. Soc, 321(1), pp.245~259 (1990)
  29. V. A. Zmorovic, "On bounds of convexity for starlike function of order in the circle jzj < 1 and in the circular region 0 < jzj < 1", Amer. Math. Soc. Transl, 80(2), pp.203~213 (1969)
  30. V. A. Zmorovic, "On the bounds of starlikeness and univalence in certain classes of functions regular in the circle jzj < 1", Amer. Math. Soc. Transl, 80(2), pp.227~242 (1966)

관련 논문AI추천

The tilted Carath\'eodory function class and its practical applications심영재, 조낙은, Inhwa Kim대한수학회 · 대한수학회보2024 · 제61권 제4호Coefficient discs and generalized central functions for the class of concave schlicht functionsBappaditya Bhowmik, Karl-Joachim Wirths대한수학회 · 대한수학회보2014 · 제51권 제5호Coefficient Bounds for a Subclass of Harmonic Mappings Con vex in One DirectionMaryam Yazdi, Mohammad Mehdi Shabani, Saeed Hashemi Sababe경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제2호A sharp Carath\'{e}odory's inequality on the boundaryB\"{u}lent Nafi \"{O}rnek대한수학회 · 대한수학회논문집2016 · 제31권 제3호Uniformly Close-to-Convex Functions with Respect to Conju gate PoinsImtiaz Ahmad, Muhammad Ishaq, Shah Muhammad, Syed Zakar Hussain Bukhari, Taimoor Salahuddin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제2호Higher-order Schwarzian derivatives of starlike functions with respect to symmetrical points and a subclass of functions with bounded turningHari Mohan Srivastava, Zhenyong Hu대한수학회 · 대한수학회보2025 · 제62권 제3호

이 간행물의 다른 논문 (13건)

Special weak properties of generalized power series ringsLunqun Ouyangpp. 687-701ON ω-LIMIT SETS AND ATTRACTION OF NON-AUTONOMOUS DISCRETE DYNAMICAL SYSTEMSBin Chen, Lei Liupp. 703-713Stability of positive steady-state solutions in a delayed Lotka-Volterra diffusion systemXiang-Ping Yan, Cun-Hua Zhangpp. 715-731HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER CHn AND THE COMPLEX HEISENBERG GROUPSKyung Bai Lee, 최영기pp. 733-743Hankel Pfaffians, discriminants and Kazhdan-Lusztig basesAlain Lascouxpp. 745-763
원문 보기