References
- O. P. Ahuja and H. Silverman, A survey on spiral-like and related function classes, Math. Chronicle 20 (1991), 39-66.
- S. D. Bernardi, New distortion theorems for functions of positive real part and applications to the partial sums of univalent convex functions, Proc. Amer. Math. Soc. 45 (1974), 113-118. https://doi.org/10.1090/S0002-9939-1974-0357755-9
- P. L. Duren, Univalent Functions, Grundlehren Math. Wiss. 259, Springer-Verlag, New York, 1983.
-
S. Gelfer, On the class of regular functions which do not take on any pair of values
${\omega}$ and$-{\omega}$ , Mat. Sb. 19 (1946), 33-46. - A. W. Goodman, Univalent Functions. Vol. II, Mariner Publishing Co. Inc., 1983.
- I. Graham and G. Kohr, Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, Inc., New York, 2003.
- F. Gray and St. Ruscheweyh, Functions whose derivatives take values in a half-plane, Proc. Amer. Math. Soc. 104 (1988), no. 1, 215-218. https://doi.org/10.1090/S0002-9939-1988-0958069-6
- D. J. Hallenbeck and T. H. MacGregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Monographs and Studies in Mathematics, 22. Pitman (Advanced Publishing Program), Boston, MA, 1984.
- G. Herglotz, Uber Potenzreihen mit positivem, reellen Teil in Einheitskreis, Ber. Verh. Sachs. Akad. Wiss. Leipzig (1911), 501-511.
- F. Holland, The extreme points of a class of functions with positive real part, Math. Ann. 202 (1973), 85-87. https://doi.org/10.1007/BF01351208
- Y. C. Kim and T. Sugawa, Growth and coefficient estimates for uniformly locally univalent functions on the unit disk, Rocky Mountain J. Math. 32 (2002), no. 1, 179-200. https://doi.org/10.1216/rmjm/1030539616
- Y. C. Kim and T. Sugawa, A conformal invariant for nonvanishing analytic functions and its applications, Michigan Math. J. 54 (2006), no. 2, 393-410. https://doi.org/10.1307/mmj/1156345602
- Y. C. Kim and T. Sugawa, Norm estimates of the pre-Schwarzian derivatives for certain classes of univalent functions, Proc. Edinb. Math. Soc. (2) 49 (2006), no. 1, 131-143. https://doi.org/10.1017/S0013091504000306
- Y. C. Kim and T. Sugawa, A note on Bazilevic functions, Taiwanese J. Math. 13 (2009), no. 5, 1489-1495. https://doi.org/10.11650/twjm/1500405555
- R. A. Kortram, The extreme points of a class of functions with positive real part, Bull. Belg. Math. Soc. Simon Stevin 4 (1997), no. 4, 449-459.
- R. J. Libera, Some radius of convexity problems, Duke Math. J. 31 (1964), 143-158. https://doi.org/10.1215/S0012-7094-64-03114-X
- T. H. MacGregor, Functions whose derivative has a positive real part, Trans. Amer. Math. Soc. 104 (1962), 532-537. https://doi.org/10.1090/S0002-9947-1962-0140674-7
- M. Nunokawa, On the univalency and multivalency of certain analysis functions, Math. Z. 104 (1968), 394-404. https://doi.org/10.1007/BF01110431
- M. S. Robertson, Variational methods for functions with positive real part, Trans. Amer. Math. Soc. 102 (1962), 82-93. https://doi.org/10.1090/S0002-9947-1962-0133454-X
- M. S. Robertson, Extremal problems for analytic functions with positive real part and applications, Trans. Amer. Math. Soc. 106 (1963), 236-253. https://doi.org/10.1090/S0002-9947-1963-0142756-3
- M. S. Robertson, Radii of star-likeness and close-to-covexity, Proc. Amer. Math. Soc. 16 (1965), 847-852.
- St. Ruscheweyh, Convolution in geometric function theory, Sem. Math. Sup. 83, University of Montreal, Montreal, Quebec, Canada 1982.
- St. Ruscheweyh and V. Singh, On certain extremal problems for functions with positive real part, Proc. Amer. Math. Soc. 61 (1976), no. 2, 329-334. https://doi.org/10.1090/S0002-9939-1976-0425102-1
- K. Sakaguchi, A variational method for functions with positive real part, J. Math. Soc. Japan 16 (1964), 287-297. https://doi.org/10.2969/jmsj/01630287
- I. Schur, Uber Potenzreihen, die im Innern des Einheitskreises beschrankt sind, J. Reine Angew. Math. 147 (1917), 205-232.
- I. Schur, Uber Potenzreihen, die im Innern des Einheitskreises beschrankt sind, J. Reine Angew. Math. 148 (1918), 122-145.
- L. Spacek, Contribution a la theorie des fonctions univalentes, Casopis Pest. Mat.-Fys. 62 (1932), 12-19.
-
L.-M. Wang, Coefficient estimates for close-to-convex functions with argument
${\lambda}$ , Bull. Berg. Math. Soc. (to appear). - S. Yamashita, Gel'fer functions, integral means, bounded mean oscillation, and univalency, Trans. Amer. Math. Soc. 321 (1990), no. 1, 245-259.
-
V. A. Zmorovic, On bounds of convexity for starlike function of order
${\alpha}$ in the circle |z| < 1 and in the circular region 0 < |z| < 1, Mat. Sb. 68 (110) (1965), 518-526; English transl., Amer. Math. Soc. Transl. (2) 80 (1969), 203-213. - V. A. Zmorovic, On the bounds of starlikeness and univalence in certain classes of functions regular in the circle |z| < 1, Ukrain. Mat. Z. 18 (1966), 28-39; English transl., Amer. Math. Soc. Transl. (2) 80 (1969), 227-242.