### Starlikeness and Convexity of Certain Classes of Meromorphically Multivalent Functions

#### Abstract

The purpose of this paper is to investigate the problems of finding the order of starlikeness and the order of convexity of the products of certain meromorphically *p*-valent functions belonging to some interesting classes of *β*-uniformly *p*-valent starlike functions and *β*-uniformly *p*-valent convex functions in the open unit disk U. The main results presented in the paper are capable of being specialized suitably in order to deduce the solutions of the corresponding problems for relatively more familiar subclasses of meromorphically *p*-valent functions in U.

#### Keywords

#### Full Text:

PDF#### References

Ali, R. M. and V. Ravichandran (2010). Integral operators on Ma-Minda type starlike and convex functions. Math. Comput. Modelling 51, 601–605.

Frasin, B. A. (2011). Convexity of integral operators of p-valent functions. Math. Comput. Modelling 53, 581–586.

Goodman, A. W. (1991a). On uniformly convex functions. Ann. Polon. Math. 56, 87–92.

Goodman, A. W. (1991b). On uniformly starlike functions. J. Math. Anal. Appl. 155, 364–370.

Kanas, S. and A.Wisniowska (1999). Conic regions and k-uniformly convexity. J. Comput. Appl. Math. 105, 327–336.

Kanas, S. and A.Wisniowska (2000). Conic regions and starlike functions. Rev. Roumaine Math. Pures Appl. 45, 647–657.

Kanas, S. and H. M. Srivastava (2000). Linear operators associated with k-uniformly convex functions. Integral Transforms Spec. Funct. 9, 121–132.

Kumar, S. S., V. Ravichandran and G. Murugusundaramoorthy (2005). Classes of meromorphic p-valent parabolic functions with positive coefficients. Austral. J. Math. Anal. Appl. 2(2), 1–9. Article 3.

Kumar, V. and S. L. Shukla (1982). Certain integrals for classes of p-valent meromorphic functions. Bull. Austral. Math. Soc. 25, 85–97.

Ma, W. and D. Minda (1992). Uniformly convex functions. Ann. Polon. Math. 57, 165–175.

Murugusundaramoorthy, G. and N. Magesh (2004). A new subclass of uniformly convex functions and a corresponding subclass of starlike functions with fixed second coefficient. J. Inequal. Pure Appl. Math. 5(4), 1–10. Article 85 (electronic).

Nishiwaki, J. and S. Owa (2007). Certain classes of analytic functions concerned with uniformly starlike and convex functions. Appl. Math. Comput. 187, 350–355.

Owa, S. and J. Nishiwaki (2002). Coefficient estimates for certain classes of analytic functions. J. Inequal. Pure Appl. Math. 3(5), 1–5. Article 72 (electronic).

Rønning, F. (1991). On starlike functions associated with the parabolic regions. Ann. Univ. Mariae Curie-Skłodowska Sect. A 45, 117–122.

Rønning, F. (1993). Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc. 118, 189–196.

Rønning, F. (1994). On uniform starlikeness and related properties of univalent functions. Complex Variables Theory Appl. 24, 233–239.

Shams, S., S. R. Kulkarni and J. M. Jahangiri (2004). Classes of uniformly starlike and convex functions. Internat. J.

Math. Math. Sci. 55, 2959–2961.

Srivastava, H. M. and S. Owa (Editors) (1992). Current Topics in Analytic Function Theory. World Scientific Publishing Company. Singapore, New Jersey, London and Hong Kong.

### Refbacks

- There are currently no refbacks.