ON EXTREME POINTS OF A CERTAIN LINEAR SPACE OF LOCALLY UNIVALENT FUNCTIONS

Authors

  • KUALIDA INAYAT NOOR Mathematics Department, College of Science,P.O. Box 2455, King Saud University, Riyadh 11451, Saudi Arabia.

DOI:

https://doi.org/10.5556/j.tkjm.23.1992.4555

Keywords:

Analytic, locally univalent, extreme points, convex, bounded boundary rotation, linear space

Abstract

Let $H = (H, \oplus, \odot)$ denote the real linear space of locally univalent normalized functions in the unit disc as defined by Hornich. For $-1\le B <A\le 1$, $k>2$, the classes $V_k[A,B]$ of functions with bounded boundary rotation are introduced and this linear space structure is used to determine the extreme points of the classes $V_k[A,B]$.

References

H. Hornich, "Ein Banachraum analytischere Funktionen in Zusamrnenhang mit den sch­lichten Funktionen", Mh. Math. 73(1969), 36-45.

K. Inayat Noor, "On some univalent integral operators", J. Math. Anal. Appl. 128 (1987), 586-592.

G. Schober, "Univalent Functions-Selected Topics", Leet. Notes Math. 478, Berlin-Rei­ delberg-New York: Springer, 1975.

N. Dunford and J. Schwartz, "Linear operators I, General Theorey", Interscience, New York, 1958.

W. Koepf, "Classical families of univalent functions in the Hornich Space", Mh. Math. 100(1985), 113-120.

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Published

1992-12-01

How to Cite

NOOR, K. I. (1992). ON EXTREME POINTS OF A CERTAIN LINEAR SPACE OF LOCALLY UNIVALENT FUNCTIONS. Tamkang Journal of Mathematics, 23(4), 321–325. https://doi.org/10.5556/j.tkjm.23.1992.4555

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Papers