참고문헌
- R. M. Ali and V. Ravichandran, Uniformly convex and uniformly starlike functions, Math. Newsletter, 21(1)(2011), 16-30.
- R. M. Ali, N. E. Cho, N. K. Jain and V. Ravichandran, Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination, Filomat, 26(3) (2012), 553-561. https://doi.org/10.2298/FIL1203553A
- R. M. Ali, N. K. Jain and V. Ravichandran, Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane, Appl. Math. Comput., 218(2012), no. 11, 6557-6565. https://doi.org/10.1016/j.amc.2011.12.033
- R. M. Ali, N. Jain and V. Ravichandran, On the radius constants for classes of analytic functions, Bull. Malays. Math. Sci. Soc., 36(2) (2013), no. 1, 23-38.
- R. M. Ali, S. Nagpal and V. Ravichandran, Second-order differential subordination for analytic functions with fixed initial coefficient, Bull. Malays. Math. Sci. Soc. (2), 34(2011), no. 3, 611-629.
- M. Finkelstein, Growth estimates of convex functions, Proc. Amer. Math. Soc., 18(1967), 412-418. https://doi.org/10.1090/S0002-9939-1967-0214749-8
- T. H. Gronwall, On the distortion in conformal mapping when the second coefficient in the mapping function has an assigned value, Nat. Acad. Proc., 6(1920), 300-302. https://doi.org/10.1073/pnas.6.6.300
- R. M. Goel, The radius of convexity and starlikeness for certain classes of analytic functions with fixed second coefficients, Ann. Univ. Mariae Curie-Sk lodowska Sect. A, 25(1971), 33-39(1973).
- S. K. Lee, V. Ravichandran and S. Supramaniam, Applications of differential subordination for functions with fixed second coefficient to geometric function theory, Tamsui Oxford J. Math. Sci., 29(2013), no. 2, 267-284.
- C. P. McCarty, Two radius of convexity problems, Proc. Amer. Math. Soc., 42(1974), 153-160. https://doi.org/10.1090/S0002-9939-1974-0325949-4
-
C. P. McCarty, Functions with real part greater than
${\alpha}$ , Proc. Amer. Math. Soc., 35(1972), 211-216. - R. Mendiratta and V. Ravichandran, Livingston problem for close-to-convex functions with fixed second coefficient, Jnanabha, 43(2013), 107-122.
- R. Mendiratta, S. Nagpal and V. Ravichandran, Second-order differential superordination for analytic functions with fixed initial coefficient, Southeast Asian Bull. Math., 39(2015), no. 6, 851-864 .
- R. Mendiratta, S. Nagpal and V. Ravichandran, Radii of starlikeness and convexity for analytic functions with fixed second coefficient satisfying certain coefficient inequalities, Kyungpook Math. J., 55(2015), no. 2, 395-410. https://doi.org/10.5666/KMJ.2015.55.2.395
- S. Nagpal and V. Ravichandran, Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions, Ann. Polon. Math., 105(2012), no. 3, 225-238. https://doi.org/10.4064/ap105-3-2
- Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1952.
- S. Owa and H. M. Srivastava, Some generalized convolution properties associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 3(2002), no. 3, Article 42, 13 pp.
- K. S. Padmanabhan and M. S. Ganesan, A radius of convexity problem, Bull. Austral. Math. Soc., 28(1983), no. 3, 433-439. https://doi.org/10.1017/S0004972700021146
- F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118(1993), no. 1, 189-196. https://doi.org/10.1090/S0002-9939-1993-1128729-7
- T. N. Shanmugam and V. Ravichandran, Certain properties of uniformly convex functions, in Computational Methods and Function Theory 1994 (Penang), 319-324, Ser. Approx. Decompos., 5 World Sci. Publ., River Edge, NJ.
- V. Singh and R. M. Goel, On radii of convexity and starlikeness of some classes of functions, J. Math. Soc. Japan, 23(1971), 323-339. https://doi.org/10.2969/jmsj/02320323
- J. Soko l and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. No. 19 (1996), 101-105.
- P. D. Tuan and V. V. Anh, Radii of convexity of two classes of regular functions, Bull. Austral. Math. Soc., 21(1980), no. 1, 29-41. https://doi.org/10.1017/S0004972700011278
- B. A. Uralegaddi, M. D. Ganigi and S. M. Sarangi, Univalent functions with positive coefficients, Tamkang J. Math., 25(1994), no. 3, 225-230.