On a class of meromorphic functions defined by the convolution

In the present paper we define some classes of meromorphic functions with fixed argument of coefficients. Next we obtain coefficient estimates, distortion theorems, integral means inequalities, the radii of convexity and starlikeness and convolution properties for the defined class of functions.

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1. J. Dziok, Classes of functions defined by certain differential-integral operators, J. Comput. Appl. Math. 105(1999), 245–255.
2. J. Dziok, Classes of p-valent analytic functions with fixed argument of coefficients, Demonstratio Math. 33(2000), 55–63.
3. J. Dziok , H. M. Srivastava, Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function, Adv. Stud. Contemp. Math., 2002, 5:115–125.
4. J. Dziok, J. Stankiewicz, On a class of p-valent analytic functions with fixed argument of coefficients defined by fractional calculus, Folia Scient. Univ. Tech. Resov. 21(1997), 19–35.
5. J. Stankiewicz. J. Waniurski, Some classes of univalent functions subordinate to linear transformation and their applications, Ann. Univ. Mariae Curie-Skl odowska, 1974, 9:85–94.
6. W. Rogosin´ski, On the coefficients of subordinate functions, Proc. Lond. Math. Soc., 1943, 48:48–82.
7. J. E. Littlewood, On inequalities in theory of functions, Proc. London Math. Soc., 1925, 23:481–519.
8. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc., 1975, 51:109–116.

9.  H. Silverman, A survey with open problems on univalent functions whose coefficients are negative, Rocky Mountain J. Math., 1991, 21:1099–1125.

10. H. Silverman, Integral means for univalent functions with negative coefficients, Houston J. Math., 1997, 23:169–174.