Examining the Function of Meromorphic with Using the Linear Convolution Operator

Öz

In this study, it is mentioned that meromorphic functions are univalent functions that are analytical everywhere. Complex analytical transformations were investigated by mentioning the necessary form for f (z) to have meromorphic function. It is a function that satisfies the condition   0 hz  . For analytic functions of f and g in the D unit disk, ()fz shows the meromorphic function class with P and subclasses of the P meromorphic analytical function class using the subordination principle between functions with the help of Hadamard product and linear operators. In this way proves is provided.

Anahtar Kelimeler

• Meromorphic function
• Univalent function
• Hadamard product

Kaynakça

1. Alexander JW, 1915. Functions which map the interior of the unit circle upon simple regions, Annals of Math. 17, 15-22.
2. Cho NE, Owa S, 2004. Partial Sums of certain meromorphic functions, J. Inequal. Pure and Appl. Math., 5(2) Art. 30.
3. Cho NE, Kim IH, 2007. Inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function, Appl. Math. Compu., 187 (1), 115 121.
4. Dziok J, Srivastava HM, 2003. Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (1) ,7-18.
5. Gonchar AA, Havin VP, Nikolski NK, 2001. Complex Analysis I. Springer-Verlag, pp 4, Newyork.Goodman A W, 1983. Univalent functions, Vol. I, Mariner Publ. Co., Tampa, FI..
6. Krantz SG, 1999. Handbook of Complex Variables, , Birkhuser, Boston, MA.
7. Liu J, Owa S, 1998. On certain meromorphic p-valent functions, Taiwanese J. Math. 2(1) , pp. 107-110.
8. MacGregor TH, Thomas HA, 1974/75. Subordination for convex functions of order . J. London Math. Soc. (2) 9, 530-536.

9. Marx A, 1936. Untersuchungen ¸ber schlichte Funktionen, Math. Ann. 107, 40-67.
10. Miller SS, Mocanu PT, 1985. On some classes of first order differential subordinations, Michigan Math. J. , 32 ,185-195.
11. Miller J, 1970. Convex meromorphic mappings and related functions, Proc. Amer. Math. Soc., 25 , 220-228.
12. Mogra L, 1991. Hadamard product of certain meromorphic univalent functions, J. Math. Anal. Appl., 157 ,10-16.
13. Nevanlinna R, 1921. über die konforme Abbildung von Sterngebieten, Ofvers. Finska 58 Vet. Soc. Förh., 53 (A), Nr. 6.
14. Nunokawa M, Ahuja OP, 2001. On meromorphic starlike and convex functions, Indian Pure Appl. Math., 32(7), 1027-1032.
15. Pommerenke Ch, 1963. On meromorphic starlike functions. Pacific J. Math. 13 221-235.
16. Royster WC, 1963. Meromorphic Starlike, Trans. Amer. Math. Soc. Vol. 107, No. 2 , pp. 300-308.
17. Srivastava HM, Owa S, 1986. A certain one parameter additive family of operators defined on analytic functions, Journal of mathematıcal analysıs and applıcatıons 118, 80-87.
18. Strohhacker E, 1933. Beitrage zur Theorie der schlichten Funktionen, Math. Z. 37, 356-380.