RADII PROBLEMS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH FIXED SECOND COEFFICIENTS

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 3,  2015, pp.317-323
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.3.317
Title & Authors
RADII PROBLEMS OF CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS WITH FIXED SECOND COEFFICIENTS
PORWAL, SAURABH; BULUT, SERAP;

Abstract
The purpose of the present paper is to study certain radii problems for the function $\small{f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}$$z^{\gamma}[D^nF(z)}$$\small{]}$$\small{^{\beta}$$^{\prime}\}$$\small{]}$$\small{^{1/{\beta}}}$, where $\small{{\beta}}$ is a positive real number, $\small{{\gamma}}$ is a complex number such that $\small{{\gamma}+{\beta}{\neq}0}$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.
Keywords
Analytic;Univalent;Starlike functions;Convex functions;Close-to-Convex functions;Spiral-like functions;Salagean Derivative;
Language
English
Cited by
References
1.
H.S. Al-Amiri, On the radius of univalence of certain analytic functions, Colloq. Math., 28 (1973), 133-139.

2.
P.L. Duren, Univalent Functions, Grundleherem der Mathematischen Wissenchaften 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.

3.
V.P. Gupta, P.K. Jain and I. Ahmad, On the radius of univalence of certain classes of analytic functions with fixed second coefficients, Rend. Math., 12 (1979), 423-430.

4.
E. Kadioglu, On subclass of univalent functions with negative coefficients, Appl. Math. Comput., 146 (2003), 351-358.

5.
V. Kumar, On univalent functions with fixed second coefficient, Indian J. Pure Appl. Math., 14(11) (1983), 1424-1430.

6.
R.J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16(1965), 755-758.

7.
A.E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17 (1966), 352-357.

8.
Z. Nehari, Conformal Mapping, Mc-Graw Hill, New York, 1953.

9.
M.S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), 374 408.

10.
G.S. Salagean, Subclasses of univalent functions, Complex Analysis-Fifth Romanian Finish Seminar, Bucharest, 1(1983), 362-372.

11.
L. Spacek, Prispevek k teorii funkciprostych, Casopispest. Math., 62 (1933), 12-19.

12.
P.D. Tuan and V.V. Anh, Radii of starlikeness and convexity of certain classes of analytic functions, J. Math. Anal. Appl., 64 (1978), 146-158.

13.
P.D. Tuan and V.V. Anh, Radii of convexity of two classes of regular functions, Bull. Aust. Math. Soc., 21 (1980), 29-41.