Document Type : Research Paper


1 Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran.

2 Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran.


In the present paper, we introduce and investigate some properties of two subclasses $ \Lambda_{n}( \lambda , \beta ) $ and $ \Lambda_{n}^{+}( \lambda , \beta ) $;  meromorphic and starlike  functions of order $ \beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.


Main Subjects

[1] S.K. Chatterjea, On starlike functions, J. Pure Math., 1 (1981) 23-26.
[2] C.Y. Gao, S.M. Yuan, and H.M. Srivastava, Some functional inequalities and inclusion relationships associated with certain families of integral operators, Comput. Math. Appl., 49 (2005) 1787-1795.
[3] A.W. Goodman, Univalent Functions, Vol. 1, Polygonal Publishing House, Washington, NJ, 1983.
[4] I. Graham and G. Kohr, Geometric Function Theory in One and Higher Dimensions, Marcel Dekker, New York, 2003.
[5] Z. Lewandowski, S.S. Miller, and E. Zlotkiewicz, Generating functions for some classes of univalent functions, Proc. Amer. Math. Soc., 65 (1976) 111-117.
[6] J.L. Li and S. Owa, Sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 33 (2002) 313-318.
[7] M.S. Liua, Y.C. Zhub, and H.M. Srivastava, Properties and characteristics of certain subclasses of starlike functions of order β, Mathematical and Computer Modelling., 48(2008) 402-419.
[8] M. Obradovi´c and S.B. Joshi, On certain classes of strongly starlike functions, Taiwanese J. Math., 2 (1998) 297-302.
[9] S. Owa, M. Nunokawa, H. Saitoh, and H.M. Srivastava, Close-to-convexity, starlikeness and convexity of certain analytic functions, Appl. Math. Lett., 15 (2002) 63-69.
[10] C. Ramesha, S. Kumar, and K.S. Padmanabhan, A sufficient condition for starlikeness, Chinese J. Math., 23 (1995) 167-171.
[11] V. Ravichandran, C. Selvaraj, and R. Rajalaksmi, Sufficient conditions for starlike functions of order α, J. Inequal. Pure Appl. Math., 3 (5) (2002) 1-6., Article 81 (electronic).
[12] S. Ruscheweyh and T. Sheil-Small, Hadamard products of schlicht functions and the P´olya-Schoenberg conjecture, Comment. Math. Helv., 48 (1973) 119-130.
[13] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 51 (1975) 109-116.
[14] H.M. Srivastava, S. Owa, and S.K. Chatterjea, A note on certain classes of starlike functions, Rend. Sem. Mat. Univ. Padova., 77 (1987) 115-124.
[15] H.M. Srivastava and M. Saigo, Multiplication of fractional calculus operators and boundary value problems involving the Euler–Darboux equation, J. Math. Anal. Appl., 121 (1987) 325-369.
[16] H.M. Srivastava, M. Saigo, and S. Owa, A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl., 131 (1988) 412-420.