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Bounded functions with positive real part. (English) Zbl 0242.30009


MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50 Coefficient problems for univalent and multivalent functions of one complex variable
30D50 Blaschke products, etc. (MSC2000)
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References:

[1] C. Carathéodory: Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen. Rend. Cire. Mat. Palermo, 32 (1911), 193 - 217. · JFM 42.0429.01 · doi:10.1007/BF03014795
[2] J. Clunie: On meromorphic schlicht functions. J. London Math. Soc, 34 (1959), 215-216. · Zbl 0087.07704 · doi:10.1112/jlms/s1-34.2.215
[3] R. M. Goel: A class of close-to convex functions. Czechoslovak Math. J., 18 (93), (1968) 104-116. · Zbl 0165.09403
[4] W. Janowski: On the radius of starlikeness of some families of regular functions. Bull. de I’Acad. Polonaise des Sciences, Ser. des sci., math. astr. et phys. XVII, (1969), 503-508. · Zbl 0185.14803
[5] W. Janowski: Extremal problems for a family of functions with positive real part and for some related families. Bull. de TAcad. Polonaise des Sciences, Ser. des sci., math., astr. et phys. XVII, (1969), 633-637. · Zbl 0191.37401
[6] J. Kaczmarski: On the coefficients of some classes of starlike functions. Bull. de I’Acad. Polonaise des Sciences, Ser. des sci., math., astr. et phys., XVII, (1969), 495-501. · Zbl 0186.39803
[7] R. J. Libera: Some radius of convexity problems. Duke Math. J., 31, (1964), 143-157. · Zbl 0129.29403 · doi:10.1215/S0012-7094-64-03114-X
[8] R. J. Libera: Univalent a-spiral functions. Canadian J. Math., 19 (1967), 449-456. · Zbl 0181.08104 · doi:10.4153/CJM-1967-038-0
[9] Z. Nehari: Conformal mapping. · Zbl 0048.31503
[10] Ch. Pommerenke: On meromorphic starlike functions. Pacific J. Math., 13, (1963), 221 - 235. · Zbl 0116.05701 · doi:10.2140/pjm.1963.13.221
[11] M. S. Robertson: On the theory of univalent functions. Ann. of Math., 37, (1936), 374-408. · Zbl 0014.16505 · doi:10.2307/1968451
[12] R. Singh: On a class of star-like functions. J. Indian Math. Soc, XXXII, (1963), 207-213. · Zbl 0199.40401
[13] J. Zamorski: About the extremal spiral schlicht functions. Ann. Polon. Math., 9 (1962), 265-273. · Zbl 0111.07602
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