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DIFFERENTIAL SUBORDINATIONS FOR CLASSES OF MEROMORPHIC p-VALENT FUNCTIONS DEFINED BY MULTIPLIER TRANSFORMATIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  05 April 2011

R. M. EL-ASHWAH ,
M. K. AOUF  and
T. BULBOACĂ
R. M. EL-ASHWAH
Affiliation:
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt (email: [email protected])
M. K. AOUF
Affiliation:
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt (email: [email protected])
T. BULBOACĂ*
Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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We investigate several inclusion relationships and other interesting properties of certain subclasses of p-valent meromorphic functions, which are defined by using a certain linear operator, involving the generalized multiplier transformations.

Keywords

multiplier transformationsmeromorphic functionsdifferential subordination

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 3 , June 2011 , pp. 353 - 368
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Aouf, M. K. and Hossen, H. M., ‘New criteria for meromorphic p-valent starlike functions’, Tsukuba J. Math. 17 (1993), 481–486.CrossRefGoogle Scholar
[2]Cho, N. E., Kwon, O. S. and Srivastava, H. M, ‘Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators’, J. Math. Anal. Appl. 242 (2004), 470–480.Google Scholar
[3]Cho, N. E., Kwon, O. S. and Srivastava, H. M, ‘Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations’, J. Math. Anal. Appl. 300 (2004), 505–520.CrossRefGoogle Scholar
[4]Cho, N. E., Kwon, O. S. and Srivastava, H. M., ‘Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations’, Integral Transforms Spec. Funct. 16(18) (2005), 647–659.Google Scholar
[5]Hallenbeck, D. J. and Ruscheweyh, St., ‘Subordinations by convex functions’, Proc. Amer. Math. Soc. 52 (1975), 191–195.Google Scholar
[6]Liu, J.-L. and Srivastava, H. M., ‘A linear operator and associated families of multivalent functions’, J. Math. Anal. Appl. 259 (2001), 566–581.CrossRefGoogle Scholar
[7]Liu, J.-L. and Srivastava, H. M., ‘Subclasses of meromorphically multivalent functions associated with a certain linear operator’, Math. Comput. Modelling 39 (2004), 35–44.Google Scholar
[8]MacGregor, T. H., ‘Radius of univalence of certain analytic functions’, Proc. Amer. Math. Soc. 14 (1963), 514–520.Google Scholar
[9]Miller, S. S. and Mocanu, P. T., ‘Second order differential inequalities in the complex plane’, J. Math. Anal. Appl. 65 (1978), 289–305.Google Scholar
[10]Miller, S. S. and Mocanu, P. T., Differential Subordinations. Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, 225 (Marcel Dekker Inc., New York, 2000).CrossRefGoogle Scholar
[11]Mogra, M. L., ‘Meromorphic multivalent functions with positive coefficients. I’, Math. Japon. 35(1) (1990), 1–11.Google Scholar
[12]Mogra, M. L., ‘Meromorphic multivalent functions with positive coefficients. II’, Math. Japon. 35(6) (1990), 1089–1098.Google Scholar
[13]Pap, M., ‘On certain subclasses of meromorphic m-valent close-to-convex functions’, Pure Math. Appl. 9 (1998), 155–163.Google Scholar
[14]Pashkouleva, D. Ž., ‘The starlikeness and spiral-convexity of certain subclasses of analytic functions’, in: Current Topics in Analytic Function Theory (eds. Srivastava, H. M. and Owa, S.) (World Scientific Publishing Company, Singapore, 1992).Google Scholar
[15]Singh, R. and Singh, S., ‘Convolution properties of a class of starlike functions’, Proc. Amer. Math. Soc. 106 (1989), 145–152.Google Scholar
[16]Srivastava, H. M. and Patel, J., ‘Applications of differential subordination to certain classes of meromorphically multivalent functions’, J. Inequal. Pure Appl. Math. 6(3) (2005), 15.Google Scholar
[17]Stankiewicz, J. and Stankiewicz, Z., ‘Some applications of the Hadamard convolution in the theory of functions’, Ann. Univ. Mariae Curie-Sklodowska Sect. A 40 (1986), 251–265.Google Scholar
[18]Uralegaddi, B. A. and Somanatha, C., ‘New criteria for meromorphic starlike univalent functions’, Bull. Aust. Math. Soc. 43 (1991), 137–140.Google Scholar
[19]Whittaker, E. T. and Watson, G. N., A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions: With an Account of the Principal Transcendental Functions, 4th edn (Cambridge University Press, Cambridge, 1927).Google Scholar
[20]Yang, D.-G., ‘Certain convolution operators for meromorphic functions’, South East Asian Bull. Math. 25 (2001), 175–186.Google Scholar