On sandwich theorems for p-valent functions involving a new generalized differential operator

Authors

Keywords:

Analytic functions, differential subordination, differential superordination, sandwich theorems.

Abstract

A new differential operator … is introduced for functions of the form f(z) = zp +1X n=2 anzn which are p-valent in the unit disk U = fz 2 C : jzj < 1g: The main object of this paper is to derive some subordination and superordination results involving differential operator Fm f(z).

Mathematics Subject Classification (2010): 30C45.

References

Ali, R.M., Ravichandran, V., Khan, M.H., Subramanian, K.G., Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci., 15(2004), no. 1, 87-94.

Al-Abbadi, M.H., Darus, M., Differential subordination defined by new generalised derivative operator for analytic functions, Int. J. Math. Math. Sci., 2010(2010), Article ID 369078, 15 pages.

Al-Oboudi, F.M., On univalent functions defined by a generalized Salagean operator, J. Math. Math. Sci., 27(2004), 1429-1436.

Bulboaca, T., Classes of first-order differential superordinations, Demonstratio Math., 35(2002), no. 2, 287-292.

Bulboaca, T., Differential Subordinations and Superordinations, Recent Results, House of Science Book Publ. Cluj-Napoca, 2005.

Darus, M., Faisal, I., Differential subordination for meromorphic multivalent quasi-convex functions, Facta Universitatis (NIS), Ser. Math. Inform., 26(2011), 1-7.

Ibrahim, R.W., Certain problems related to classes of analytic functions and applications, PhD Thesis, Universiti Kebangsaan Malaysia, 2010.

Ibrahim, R.W., Darus, M., Subordination and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl., 345(2008), no. 2, 871-879.

Ibrahim, R.W., Darus, M., On subordination theorems for new classes of normalize analytic functions, Appl. Math. Sci., 56(2008), no. 2, 2785-2794.

Ibrahim, R.W., Darus, M., Differential subordination for meromorphic multivalent quasi-convex functions, Acta Mathematica Universitatis Comenianae, 79(2010), no. 1, 39-45.

Ibrahim, R.W., Darus, M., Subordination for meromorphic functions defined by an operator, Int. J. Pure and Appl. Math., 69(2011), no. 4, 413-419.

Darus, M., Al-Shaqsi, K., On Subordinations for certain analytic functions associated with generalized integral operator, Lobachevskii Journal of Mathematics, 29, no. 2, 90-97.

Miller, S.S., Mocanu, P.T., Differential Subordination, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 2000.

Miller, S.S., Mocanu, P.T., Subordinants of differential superordinations, Complex Var. Theory Appl., 48(2003), no. 10, 815-826.

Mohammed, A., Darus, M., Breaz, D., On subordination, starlikeness and convexity of certain integral operators, Mathematica, 76(2011), no. 2, 165-170.

Mohd, M.H., Darus, M., Differential subordination and superordination for Srivastava-Attiya operator, Int. J. Differential Equations, 2011 (2011), Article ID 902830, 19 pages.

Salagean, G.S., Subclasses of univalent functions, Lecture Notes in Mathematics, 1013(1983), 362-372.

Shanmugan, T.N., Ramachandran, C., Darus, M., Sivasubbramanian, S., Differential sandwich theorems for some subclasses of analytic functions involving a linear operator, Acta Math. Univ. Comenian., 74(2007), no. 2, 287-294.

Shanmugam, T.N., Ravichandran, V., Sivasubramanian, S., Differential sandwhich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl., 3(2006), no. 1, 1-11.

Shanmugam, T.N., Srikandan, S., Frasin, B.A., Kavitha, S., On sandwich theorems for certain subclasses of analytic functions involving carlson-shaer operator, J. Korean Math. Soc., 45(2008), no. 3, 611-620.

Shanmugam, T.N., Sivasubramanian, S., Silverman, H., On sandwhich theorems for some classes of analytic functions, Int. J. Math. Math. Sci., Article ID 29684, (2006), 1-13.

Sivasubramanian, S., Mohammed, A., Darus, M., Certain subordination properties for subclasses of analytic functions involving complex order, Abstract and Applied Analysis, 2011 (2011), Article ID 375897, 8 pages.

Tuneski, N., On certain sufficient conditions for starlikeness, Int. J. Math. Math. Sci., 23(2000), no. 8, 521-527.

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Published

2015-09-30

How to Cite

Al-HAWARY, T., FRASIN, B., & DARUS, M. (2015). On sandwich theorems for p-valent functions involving a new generalized differential operator. Studia Universitatis Babeș-Bolyai Mathematica, 60(3), 395–402. Retrieved from https://studia.reviste.ubbcluj.ro/index.php/subbmathematica/article/view/5779

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