On inclusion relationships of certain subclasses of meromorphic functions involving integral operator

Ali Muhammad

Abstract


In this paper, we introduce some subclasses of meromorphic functions in the punctured unit disc. Several inclusion relationships and some other interesting properties of these classes are discussed.

Keywords


Meromorphic functions; functions with bounded boundary and bounded radius rotation; quasi-convex functions; close-to-convex functions; generalized hypergeometric functions; functions with positive real part; Hadamard product (or convolution)

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References


Carlson, B. C., Shaeffer, B. D., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), no. 4, 737-745.

Cho, N. E., Noor, K. I., Inclusion properties for certain classes of meromorphic functions associated with Choi-Saigo-Srivastava operator, J. Math. Anal. Appl. 320 (2006), no. 2, 779-786.

Cho, N. E., Kwon, O. S. and Srivastava, H. M., Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiflier transformations, Integral Transforms Spec. Funct. 16 (2005), no. 8, 647-659.

Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999), no. 1, 1-13.

Hohlov, E. Y., Operators and operations in the class of univalent functions, Izv. Vyssh. Uchebn. Zaved. Mat., (1978), no. 10 (197), 83-89 (in Russian).

Jung, I. B., Kim, Y. C. and Srivastava, H. M., The Hardy space of analytic functions associated with certain one-parameter families of integral operators, J. Math. Anal. Appl. 176 (1993), no. 1, 138-147.

Kumar, V., Shukla, S. L., Certain integrals for classes of p-valent meromorphic functions, Bull. Austral. Math. Soc. 25 (1982), no. 1, 85-97.

Miller, S. S., Differential inequalities and Caratheodory functions, Bull. Amer. Math. Soc. 81 (1975), 79-81.

Noor, K. I., On certain classes of meromorphic functions involving integral operators, JIPAM. J. Inequal. Pure Appl. Math. 7 (2006), no. 4, Article 138, 8 pp. (electronic).

Noor, K. I., On subclasses of close-to-convex functions of higher order, Internat. J. Math. Math. Sci. 15 (1992), no. 2, 279-290.

Noor, K. I., On new classes of integral operators, J. Nat. Geom. 16 (1999), no. 1-2, 71-80.

Noor, K. I., On close-to-convex and related functions, Ph. D. Thesis, University of Wales, Swansea, U. K., 1972.

Noor, K. I., On quasiconvex functions and related topics, Internat. J. Math. Math. Sci. 10 (1987), no. 2, 241-258.

Noor, K. I., Noor, M. A., On integral operators, J. Math. Anal. Appl. 238 (1999), no. 2, 341-352.

Noor, K. I., Thomas, D. K., Quasiconvex univalent functions, Internat. J. Math. Math. Sci. 3 (1980), no. 2, 255-266.

Padmanabhan, K., Parvatham, R., Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math. 31 (1975/76), no. 3, 311-323.

Pinchuk, B., Functions of bounded boundary rotation, Israel J. Math. 10 (1971), 6-16.

Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109-115.

Selvaraj, C., Karthikeyan, K. R., Some inclusion relationships for certain subclasses of meromorphic functions associated with a family of integral operators, Acta Math. Univ. Comenian. (N. S.) 78 (2009), no. 2, 245-254.

Yuan, S.-M., Liu, Z.-M. and Srivastava, H. M., Some inclusion relationships and integral-preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators, J. Math. Anal. Appl. 337 (2008), no.1, 505-515.




DOI: http://dx.doi.org/10.17951/a.2012.66.1.63-73
Data publikacji: 2016-07-24 20:22:25
Data złożenia artykułu: 2016-07-24 16:15:36

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Copyright (c) 2012 Ali Muhammad