Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843 - 7265 (print)
 Volume 3 (2008), 67 -- 77

SUBCLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS DEFINED BY RUSCHEWEYH DERIVATIVE II

Waggas Galib Atshan

Abstract. New class Σλ(α, β, γ) of univalent meromorphic functions defined by Ruscheweyh derivative in the punctured unit disk U* is introduced. We study several Hadamard product properties. Some results connected to inclusion relations, neighborhoods of the elements of class Σλ(α, β, γ) and integral operators are obtained.

2000 Mathematics Subject Classification: 30C45.
Keywords: Meromorphic functions; Ruscheweyh derivative; Hadamard product; Coefficients inequalities; Integral operator; Neighborhood.

Full text

References

  1. W. G. Atshan and S. R. Kulkarni, Subclass of meromorphic functions with positive coefficients defined by Ruscheweyh derivative (I), J. Rajasthan Acad. Phy. Sci., 6(2) (2007), 129-140. MR2332617(2008d:30013).

  2. A. W. Goodman, Univalent functions and nonanalytic curve, Proc. Amer. Math. Soc., 8 (1957), 598-601. MR0086879(19,260a). Zbl 0166.33002.

  3. Jin-Lin Liu and H. M. Srivastava, A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl. 259 (2001), 566-581. MR1842079(2002i:30014). Zbl 0997.30009.

  4. S. Ruscheweyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81 (1981), 521-527. MR0601721(82c:30016). Zbl 0458.30008.

  5. B. A. Uralegaddi and M. G. Ganigi, A certain class of meromorphically starlike functions with positive coefficients, Pure Appl. Math. Sci., 26 (1987), 75-81. MR0935517(89h:30027). Zbl 0638.30014.




Waggas Galib Atshan
Department of Mathematics,
College of Computer Science and Mathematics,
Al-Qadisiya University,
Iraq.
e-mail: waggashnd@yahoo.com

http://www.utgjiu.ro/math/sma