Goodman's conjectures on the coefficients of multivalent functions

References

• Bender , J . 1962 . Some extremal theorems for multivalently star-like functions . Duke Math J. , 29 : 101 – 106 .
   Web of Science ®Google Scholar
• Bieberbach , L. 1916 . Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Albelduneg . S.B. Preuss. Aksd. Wiss , 138 : 940 – 955 .
   Google Scholar
• Biernacki , M. 1936 . Sur les fonctions multivalentes d'ordre p . Compes Rendus Hebdomadaires des Séances de I'Academie des Sciences , 203 : 449 – 451 . Paris
   Google Scholar
• Cartwright , M. L. 1935 . Some inequalities in the theory of functions . Math. Ann. , 3 : 98 – 118 .
   Google Scholar
• DeBranges , L. 1985 . A proof of the Bieberbach conjecture . Acta. Math , 154 : 137 – 152 .
   Web of Science ®Google Scholar
• Delsarte , Philippe and Genin , Yves . 1989 . A simple proof of Livingston's inequality for Caratheodory functions . proc Amer Math. Soc. , 107 : 1017 – 1020 .
   Web of Science ®Google Scholar
• Goodman , A. W. 1948 . On some determinants related to p-valent . Trans. Amer, Math Soc , 63 : 175 – 192 .
   Web of Science ®Google Scholar
• Goodman , A. W. 1950 . On the Schwarz-Christoffel transformation and p-valent functions . Trans Amer Math Soc , 68 : 204 – 223 .
   Web of Science ®Google Scholar
• Goodman , A. W. and Robertson , M. S. 1951 . A class of multivalent functions . Trans. Amer. Math. Soc. , 70 : 127 – 136 .
   Web of Science ®Google Scholar
• Goodman , A. W. 1951 . Typically real functions with assigned zeros . Proc. .Amer.Math. Soc. , 2 : 345 – 357 .
   Web of Science ®Google Scholar
• Hallenbeck , D. J. and Livingston , A. E. 1976 . A coefficient estimate for multivalent functions . Proc Amer. Math. Soc. , 54 : 201 – 206 .
   Web of Science ®Google Scholar
• Hummel , J. A. 1967 . Multivalent star-like functions . J D'Analyse Math. , 18 : 133 – 160 .
   Web of Science ®Google Scholar
• Jenkins , J. A. 1965 . Univalent functions and conformal mapping , Berlin : Springer-Verlag .
   Google Scholar
• Kaplan , W. 1952 . Close-to-convex schlicht functions . Mich. Math. J. , 1 : 169 – 185 .
   Google Scholar
• Livingston , A. E. 1965 . P-valent close-to-convex functions . Trans Amer Math Soc. , 115 : 161 – 179 .
   Web of Science ®Google Scholar
• Livingston , A. E. 1969 . The coefficients of multivalent close-to-convex functions . Proc. Amer. Math. Soc. , 21 : 545 – 552 .
   Web of Science ®Google Scholar
• Livingston , A. E. 1985 . A coefficient inequality for functions of positive real part with an application to multivalent functions . Pac J. Math. , 120 : 139 – 151 .
   Web of Science ®Google Scholar
• Livingston , A. E. 1987 . The coefficients of univalent functions related to Goodman' conjecture . J. London Math. Soc , 36 ( 2 ) : 436 – 444 .
   Google Scholar
• Livingston , A. E. 1988 . Weakly ciose-to-convex functins. . Rocky Mountain J. Math , 18 ( 2 ) : 719 – 732 .
   Google Scholar
• Lyzzaik , A. 1982 . Multivalent linearly accessible functions and close-to-convex functions . Proc London Math. Soc. , 44 ( 2 ) : 178 – 192 .
   Google Scholar
• Lyzzaik , A. and Styer , D. 1978 . Goodman's conjecture .and the coefficients of univalent functions . Proc. Amer. Math. Soc , 69 ( 2 ) : 111 – 114 .
   Google Scholar
• Nevanlina , R. 1921 . Über die konforme Abbildung von Sterngebieten . Oeversikt av Finska-Vetenskaps Societen Förhandlingar. , 63 ( A ) : 1 – 21 .
   Google Scholar
• Reade , M. O. 1953 . The coefficients of close-to-convex functions . Duke Math. J. , 20 ( A ) : 539 – 550 .
   Google Scholar
• Robertson , M. S. 1952 . A coefficient problem for functions regular in an annulus. . Canadian J. Math , 4 ( A ) : 407 – 423 .
   Web of Science ®Google Scholar
• Robertson , M. S. 1953 . Multivalently star-like functions . Duke Math.J. , 20 ( A ) : 539 – 549 .
   Google Scholar
• Spencer , D. C. 1941 . On mean one-valent functions . Ann. of Math. , 42 ( A ) : 614 – 633 .
   Google Scholar
• Styer , D. 1973 . On weakly starlike univalent functions . Ann. of Math. , 26 : 217 – 233 .
   Google Scholar
• Stver , D. 1972 . Close-to-convex multivalent functions with respect to weakly star-like functions . Trans. Amer. Math. Soc , 169 : 105 – 112 .
   Web of Science ®Google Scholar
• Umezawa , T. 1957 . Multivalently close-to-convex functions . Proc Amer. Math Soc , 8 : 869 – 874 .
   Google Scholar