A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS

Title & Authors
A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS
Kwon, Ohsang; Sim, Youngjae;

Abstract
We introduce a subclass $\small{S_s^{({\kappa})}}$(A,B) (-1 $\small{{\leq}}$ B < A $\small{{\leq}}$ 1) of functions which are analytic in the open unit disk and close-to-convex with respect to $\small{{\kappa}}$-symmetric points. We give some coefficient inequalities, integral representations and invariance properties of functions belonging to this class.
Keywords
close-to-convex functions;Janowski type;sakaguchi functions;k-symmetric points;
Language
English
Cited by
References
1.
N. E. Cho, O. S. Kwon, and S. Owa, Certain subclasses of Sakaguchi functions, Southeast Asian Bull. Math. 17 (1993), no. 2, 121-126.

2.
R. M. Goel and B. S. Mehrok, Some invariance properties of a subclass of close-to-convex functions, Indian J. Pure Appl. Math. 12 (1981), no. 10, 1240-1249.

3.
S. S. Miller and P. T. Mocanu. Differential Subordinations: Theory and Applications, Marcel Dekker Inc, New York, Basel, 1999.

4.
R. Parvatham and S. Radha, On ${\alpha}$-starlike and ${\alpha}$-close-to-convex functions with respect to n-symmetric points, Indian J. Pure Appl. Math. 17 (1986), no. 9, 1114-1122.

5.
V. Ravichandran, Starlike and convex functions with respect to conjugate points, Acta Math. Acad. Paedagog. Nyhazi. (N.S.) 20 (2004), no. 1, 31-37.

6.
K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75.

7.
T. N. Shanmugam, Convolution and differential subordination, Int. J. Math. Math. Sci. 12 (1989), no. 2, 333-340.

8.
H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math. 37 (1985), no. 1, 48-61.

9.
E. M. Silvia, Subclass of close-to-convex functions, Int. J. Math. Math. Sci. 6 (1983), no. 3, 449-458.

10.
J. Sokol et al., On some subclass of starlike functions with respect to symmetric points, Zeszyty Nauk. Politech. Rzeszowskiej Mat. Fiz. 12 (1991), 65-73.

11.
J. Stankiewicz, Some remarks on functions starlike with respect to symmertic points, Ann. Univ. Mariae Curie-Sklodowska Sect. A 19 (1970), 53-59.

12.
T. V. Sudharsan, P. Balasubrahmanyam, and K. G. Subramanian, On functions starlike with respect to symmetric and conjugate points, Taiwanese J. Math. 2 (1998), no. 1, 57-68.

13.
J. Thangamani, On starlike functions with respect to symmetric points, Indian J. Pure Appl. Math. 11 (1980), no. 3, 392-405.