본문 바로가기
KERD
논문KCI 등재

FEKETE-SZEG¨O PROBLEM FOR CERTAIN SUBCLASSES OF UNIVALENT FUNCTIONS

Allu Vasudevarao
대한수학회 (The Korean Mathematical Society)|2015.11|대한수학회보 (Bulletin of the KMS)|제52권 제6호|pp. 1937-1943

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

univalent functionsstarlikeconvexclose-to-convex and Fekete- Szeg¨o problem
주제분류수학

초록

For 1 ≤ α < 2, let F(α) denote the class of locally univalent normalized analytic functions f(z) = z + ∑∞ n=2 anzn in the unit disk D = {z ∈ C : |z| < 1} satisfying the condition Re(1 + zf′′(z)/ f′(z)) > α/2 − 1. In the present paper, we shall obtain the sharp upper bound for Fekete- Szeg¨o functional |a3 − λa22 | for the complex parameter λ.

Abstract

For 1 ≤ α < 2, let F(α) denote the class of locally univalent normalized analytic functions f(z) = z + ∑∞ n=2 anzn in the unit disk D = {z ∈ C : |z| < 1} satisfying the condition Re(1 + zf′′(z)/ f′(z)) > α/2 − 1. In the present paper, we shall obtain the sharp upper bound for Fekete- Szeg¨o functional |a3 − λa22 | for the complex parameter λ.

참고문헌 (23)

  1. H. R. Abdel-Gawad, "The Fekete-Szeg¨o problem for strongly closeto-convex functions", Proc. Amer. Math. Soc, 114(2), pp.345~349 (1992)
  2. B. Bhowmik, "On the Fekete-Szeg¨o problem for concave univalent functions", J. Math. Anal. Appl, 373(2), pp.432~438 (2011)
  3. J. H. Choi, "A general approach to the Fekete-Szeg¨o problem", J. Math. Soc. Japan, 59(3), pp.707~727 (2007)
  4. P. L. Duren, "Univalent functions" (1983), Springer-Verlag
  5. M. Fekete, "Eine Bemerkung ¨uber ungerade schlichte Funktionen", J. London Math. Soc, 8, pp.85~89 (1933)
  6. J. A. Jenkins, "A general coefficient theorem", Trans. Amer. Math. Soc, 77, pp.262~280 (1954)
  7. J. A. Jenkins, "On Certain Coefficients of Univalent Funcions, Analytic Functions" (1960), Princeton University press
  8. F. R. Keogh, "A coefficient inequality for certain classes of analytic functions", Proc. Amer. Math. Soc, 20(1), pp.8~12 (1969)
  9. Y. C. Kim, "Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions", Proc. Edinb. Math. Soc, 49(1), pp.131~143 (2006)
  10. W. Koepf, "On the Fekete-Szeg¨o problem for close-to-convex functions", Proc. Amer. Math. Soc, 101(1), pp.89~95 (1987)
  11. W. Koepf, "On the Fekete-Szeg¨o problem for close-to-convex functions II", Arch. Math. (Basel), 49(5), pp.420~433 (1987)
  12. R. R. London, "Fekete-Szeg¨o inequalities for close-to-convex functions", Proc. Amer. Math. Soc, 117(4), pp.947~950 (1993)
  13. W. Ma, "An internal geometric characterization of strongly starlike functions", Ann. Univ. Mariae Curie-Sk lodowska, Sect. A, 45, pp.89~97 (1991)
  14. W. Ma, "A unified treatment of some special classes of univalent functions", Proceedings of the Conference on Complex Analysis, pp.157~169 (1992), International Press Inc
  15. W. Ma, "Coefficient inequalities for strongly close-to-convex functions", J. Math. Anal. Appl, 205(2), pp.537~553 (1997)
  16. Y. A. Muhanna, "Extremal problems on the class of convex functions of order −1", 2, 2014, pp.103(6), 461~471
  17. Z. Nehari, "The Schwarzian derivative and schlicht functions", Bull. Amer. Math. Soc, 55, pp.545~551 (1949)
  18. A. Pfluger, "The Fekete-Szeg¨o inequality by a variational method", Ann. Acad. Sci. Fenn. Ser. A I Math, 10, pp.447~454 (1985)
  19. A. Pfluger, "The Fekete-Szeg¨o inequality for complex parameters", Complex Variables Theory Appl, 7(1-3), pp.149~160 (1986)
  20. S. Ponnusamy, "New sufficient conditions for starlike and univalent functions", Soochow J. Math, 21(2), pp.193~201 (1995)
  21. S. Ponnusamy, "Univalence of certain integral transforms", Glas. Mat. Ser. III (51), 31(2), pp.253~261 (1996)
  22. S. Ponnusamy, "Region of variability of two subclasses of univalent functions", J. Math. Anal. Appl, 332(2), pp.1323~1334 (2007)
  23. A. Vasudevarao, "An arclength problem for some subclasses of univalent functions", J. Analysis (2014)

관련 논문AI추천

Fekete-Szego Problem for a Generalized Subclass of Analytic FunctionsHalit Orhan, Murat Caglar, Nihat Yagmur경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제1호The Fekete-Szegö inequality for subclass of analytic functions of complex orderG. Murugusundaramoorthy, T. Panigrahi장전수학회 · Advanced Studies in Contemporary Mathematics2014 · 제24권 제1호On the Fekete-Szegö Problem for Starlike Functions of Complex OrderAbdel-Moniem Lashin, Bashar Al Saeedi, Hanan Darwish경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제3호Sharp coefficient inequalities for certain subclasses of bi-univalent Bazilevi\v{c} functionsAmol Bhausaheb Patil대한수학회 · 대한수학회논문집2022 · 제37권 제1호Fekete-Szego Inequalities for Quasi-Subordination Functions Classes of Complex OrderRabha El-Ashwah, Stanislawa Kanas경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호Sharp bounds for the initial coefficients for certain families of bi-univalent functionsAhmad Motamednezhad, Safa Salehian대한수학회 · 대한수학회논문집2024 · 제39권 제4호

이 간행물의 다른 논문 (21건)

A GENERALIZED ADDITIVE-QUARTIC FUNCTIONAL EQUATION AND ITS STABILITYCharinthip Hengkrawit, Anurak Thanyacharoenpp. 1759-1776ON THE LOWER SEMICONTINUITY OF THE SOLUTION SETS FOR PARAMETRIC GENERALIZED VECTOR MIXED QUASIVARIATIONAL INEQUALITY PROBLEMSNguyen Van Hungpp. 1777-1795DISCRETE MEASURES WITH DENSE JUMPS INDUCED BY STURMIAN DIRICHLET SERIES권도용pp. 1797-1803ON CERTAIN GENERALIZED q-INTEGRAL OPERATORS OF ANALYTIC FUNCTIONSKuppathai Appasamy Selvakumaran, Sunil Dutt Purohitpp. 1805-1818ON A MULTI-PARAMETRIC GENERALIZATION OF THE UNIFORM ZERO-TWO LAW IN L1-SPACESFarrukh Mukhamedovpp. 1819-1826
원문 보기