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1995 | 62 | 3 | 231-244
Tytuł artykułu

Coefficient bounds for certain classes of analytic functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We determine coefficient estimates for α-spiral functions of order ϱ with respect to N-symmetric points (|α| = π/2, 0 ≤ ϱ = 1$ and N is a positive integer). Sharp coefficient bounds are also obtained for functions of the form $f(z)^{-t}$, where t is a positive integer and f(z) is an α-spiral function of order ϱ. Using this we deduce coefficient estimates for inverses of univalent α-spiral and meromorphic univalent α-spiral functions with vanishing early coefficients.
Rocznik
Tom
62
Numer
3
Strony
231-244
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-03-24
poprawiono
1994-12-15
Twórcy
autor
  • Department of Mathematics, Indian Institute of Technology, Kanpur-208 016, India
autor
  • Department of Mathematics, University of Helsinki, P.o. Box 4, Hallituskatu 15, Fin-00014 Helsinki, Finland
  • Department of Mathematics, Crescent Engineering College, Vandalur, Madras-600 048, India
Bibliografia
  • [1] B. L. Bhatia and S. Rajasekaran, Coefficient estimates for alpha-spiral functions, Bull. Austral. Math. Soc. 28 (1983), 319-329.
  • [2] A. V. Boyd, Coefficient estimates for starlike functions of order α, Proc. Amer. Math. Soc. 17 (1966), 1016-1019.
  • [3] R. Chand and P. Singh, On certain schlicht mappings, Indian J. Pure Appl. Math. 10 (1979), 1167-1174.
  • [4] Z. J. Jakubowski, On the coefficients of starlike functions of some classes, Bull. Acad. Polon. Sci. 9 (1971), 811-815.
  • [5] O. P. Juneja and S. Rajasekaran, Coefficient estimates for inverses of α-spiral functions, Complex Variables Theory Appl. 6 (1986), 99-108.
  • [6] R. J. Libera, Univalent α-spiral functions, Canad. J. Math. 19 (1967), 449-456.
  • [7] R. J. Libera and E. J. Złotkiewicz, Early coefficients of the inverse of a regular convex function, Proc. Amer. Math. Soc. 85 (1982), 225-230.
  • [8] R. J. Libera and E. J. Złotkiewicz, Coefficient bounds for the inverse of odd univalent functions, Complex Variables Theory Appl. 3 (1983), 185-189.
  • [9] T. H. MacGregor, Coefficient estimates for starlike mappings, Michigan Math. J. 10 (1963), 277-281.
  • [10] J. T. Poole, On starlike functions, Proc. Amer. Math. Soc. 19 (1968), 495-500.
  • [11] M. S. Robertson, Applications of the subordination principle to univalent functions, Pacific J. Math. 11 (1961), 315-324.
  • [12] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75.
  • [13] G. Schober, Coefficients of inverses of meromorphic univalent functions, Proc. Amer. Math. Soc. 67 (1977), 111-116.
  • [14] G. Schober, Coefficient estimates for the inverses of schlicht functions, in: Aspects of Contemporary Complex Analysis, Academic Press, New York, 1980, 503-513.
  • [15] P. Singh and P. Singh, Integral representations of functions in certain classes of univalent functions, Indian J. Pure Appl. Math. 12 (1981), 459-471.
  • [16] L. Špaček, Contributions à la théorie des fonctions univalentes, Časopis Pěst. Mat. 62 (1933), 12-19 (in Czech).
  • [17] R. S. L. Srivastava, Univalent spiral functions, in: Topics in Analysis, Lecture Notes in Math. 419, Springer, Berlin, 1974, 327-341.
  • [18] J. Stankiewicz and J. Waniurski, Some classes of functions subordinate to linear transformation and their applications, Ann. Univ. M. Curie-Skłodowska 28 (9) (1974), 85-94.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv62z3p231bwm
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