On radii of convexity and starlikeness of some classes of functions

V. SINGH; R. M. GOEL

doi:10.2969/jmsj/02320323

V. SINGH, R. M. GOEL

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1971 Volume 23 Issue 2 Pages 323-339

DOI https://doi.org/10.2969/jmsj/02320323

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Published: 1971 Received: June 01, 1970 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : V. SINGH¹⁾, R.M. GOEL¹⁾
Right : V. SINGH¹⁾, R. M. GOEL¹⁾

Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M. S. Robertson, Extremal problems for analytic functions with positive real part and applications, Trans. Amer. Math. Soc., 106 (1963), 236-253.
2) M. S. Robertson, Variational methods for functions with positive real part, Trans. Amer. Math. Soc., 101 (1962), 82-93.
3) V. A. Zmorovic, On bound of convexity for starlike functions of order α in the circle |z|<1 and in 0<|z|<1, Mat. Sb. (N.S.), 68 (110) (1965), 518-526.
4) A. Schild, On starlike functions of order α, Amer. J. Math., 87 (1965), 65-70.
5) K. S. Padmanabhan, On the radius of convexity of certain class of meromorphically starlike functions in the unit circle, Math. Z., 91 (1966), 308-313.
6) K. Sakaguchi, A variational method for functions with positive real part, J. Math. Soc. Japan, 16 (1964), 287-297.
7) A. E. Livingston, On the radius of univalence of certain analytic functions,. Proc. Amer. Math. Soc., 17 (1966), 352-357.
8) C. Caratheodory, Theory of functions, vol. 2, New York, 1954.
9) Z. Nehari, Conformal mapping, McGraw-Hill Book Co., New York, 1954.

Right : [1] M. S. Robertson, Extremal problems for analytic functions with positive real part and applications, Trans. Amer. Math. Soc., 106 (1963), 236-253.
[2] M. S. Robertson, Variational methods for functions with positive real part, Trans. Amer. Math. Soc., 101 (1962), 82-93.
[3] V. A. Zmorovic, On bound of convexity for starlike functions of order α in the circle |z|<1 and in 0<|z|<1, Mat. Sb. (N. S.), 68 (110) (1965), 518-526.
[4] A. Schild, On starlike functions of order α, Amer. J. Math., 87 (1965), 65-70.
[5] K. S. Padmanabhan, On the radius of convexity of certain class of meromorphically starlike functions in the unit circle, Math. Z., 91 (1966), 308-313.
[6] K. Sakaguchi, A variational method for functions with positive real part, J. Math. Soc. Japan, 16 (1964), 287-297.
[7] A. E. Livingston, On the radius of univalence of certain analytic functions,. Proc. Amer. Math. Soc., 17 (1966), 352-357.
[8] C. Caratheodory, Theory of functions, vol. 2, New York, 1954.
[9] Z. Nehari, Conformal mapping, McGraw-Hill Book Co., New York, 1954.

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