CERTAIN SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH POSITVE OR NEGATIVE COEFICIENTS USING DIFFERENTIAL OPERATOR

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Hazha Zirar Hussain

Abstract

In this paper, we have introduced two subclasses  and  of meromorphically p-valent functions with positive and negative coefficients, defined by differential operator in the punctured unit disk  and obtain some sharp results including coefficient inequality, distortion theorem, radii of starlikeness and convexity, closure theorems of these subclasses of meromorphically p-valent functions. We also derive some interesting results for the Hadamard products of functions belonging to the classes  and .

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How to Cite
Hazha Zirar Hussain. (2023). CERTAIN SUBCLASSES OF MEROMORPHICALLY P-VALENT FUNCTIONS WITH POSITVE OR NEGATIVE COEFICIENTS USING DIFFERENTIAL OPERATOR. Tikrit Journal of Pure Science, 21(6), 173–179. https://doi.org/10.25130/tjps.v21i6.1098
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References

[1] O. Altintas, H. Irmark, H. M. Srivastava, A family of meromorphically univalent functions with positive coefficients, Panamer.Math. J. 5(1)(1995), 75-81.

[2] M. K. Aouf, A. E. Shammaky, A certain subclass of meromorphically p-valent starlike functions with negative coefficients, J. Approx. Theory Appl. 1(2)(2005), 123-143.

[3] M. P. Chen, H. Irmark, H. M. Srivastava, C, S, Yu, Certain subclasses of meromorphically univalent functions with positive or negative coefficients, Panamer. Math. J. 6(2)(1996), 65-77.

[4] N. E. Cho. S. Lee, S. Owa, A class of meromorphic univalent functions with positive coefficients, Kobe J. Math. 4 (1987), 43-50.

[5] N. E. Cho, S. Owa, S. H. Lee,O. Altinats, Generalization class of certain meromorphic univalent functions with positive coefficients, Kyungpook Math. J. 29 (1989), 133-139.

[6] P. L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.

[7] A. W. Goodman, Univalent Functions, vols. I, II, Polygenal Publishing House, Washinton, NJ. 1983.

[8] F. Ghanim, M. Darus, On certain class of analytic function with fixed second positive coefficient, International Journal of Mathematical Analysis, vol. 2, nl. 2, 55-66, 2008.

[9] F. Ghanim , M. Darus, Some subordination results associated with certain subclass of analytic meromorphic functions, Journal of Mathematics and Statistics, vol. 4, no. 2, 112-116, 2008.

[10] F. Ghanim , M. Darus and S. Sivasubramanian, On new subclass of analytic univalent function, International Journal of Pure and Applied Mathematics, vol. 40, no. 3, pp. 307- 319, 2007.

[11] S. B. Joshi, S. R. Kulkarni, H. M. Srivastava, Certain classes of meromorphic functions with positive and missing coefficients, J. Math. Anal. Appl. 193 (1995), 1-14.

[12] J. L. Liu, Properties of some families of meromorphic p-valent functions, Math. Japonica, 52 (2000), 425-434.

[13] J. L. Liu, H. M. Srivastava, A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl. 259 (20000), 566-581.

[14] J. L. Liu, H. M. Srivastava, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function, Math. Comput.Modelling, 30(2004), 21-34.

[15] R. K. Raina, H. M. Srivastava, A new class of meromorphically multivalent functions with applications to generalized hypereometric functions, Math. Comput.Modelling, 43 (2006), 350-356.

[16] A. Schild, H. Silverman, Convolution of univalent functions with negative coefficients, Ann. Uni. Mariae Curie-Sklodowska Sect. A 29 (1975), 99-107.

[17] H. M. Srivastava, H. M. Hossen, M. K. Aouf, A certain subclass of meromorphically convex functions with negative coefficients, Math. J. Ibaraki Univ. 30(1998), 33-51.

[18] H. M. Srivastava, S. Owa(Eds.), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Sinapore, New Jersey, London, Hong Kong, 1992.

[19] B. A. Uralegaddi, M. D. Ganigi, Meromorphic convex functions with negative coefficients, J. Math. Res. Exposition 1 (1987), 21-26.