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Abstrakty
In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.
Czasopismo
Rocznik
Tom
Strony
97--109
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
- Department of Mathematics, Department of Mathematics, Faculty of Science, Faculty of Science Fayoum University, Fayoum 63514, Egypt
autor
- Department of Mathematics, Faculty of Science, Faculty of Science Fayoum University, Fayoum 63514, Egypt Mansoura 35516
Bibliografia
- [1] R. M. Ali, V. Ravichandran and K. G. Subramanian, Differential sandwich theorems for certain analytic functions, Far East J. Math. Sci. 15 (2004), no. 1, 87-94.
- [2] F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Internat. J. Math. Math. Sci., 27 (2004), 1429-1436.
- [3] M. K. Aouf and A. O.Mostafa, Sandwich theorems for analytic functions defined by convolution, Acta Univ. Apulensis, 21(2010), 7-20.
- [4] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429–446.
- [5] T. Bulboaca, Classes of first order differential superordinations, Demonstratio Math. 35 (2002), no. 2, 287-292.
- [6] T. Bulboaca, Differential Subordinations and Superordinations, Recent Results, House of Scientific Book Publ., Cluj-Napoca, 2005.
- [7] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal., 15 (1984), 737-745.
- [8] A. Catas, G. I. Oros and G. Oros, Differential subordinations associated with multiplier transformations, Abstract Appl. Anal., 2008 (2008), ID 845724, 1-11.
- [9] N. E. Cho and T. G. Kim, Multiplier transformations and strongly close-toconvex functions, Bull. Korean Math. Soc., 40 (2003), no. 3, 399-410.
- [10] J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103 (1999), 1-13.
- [11] J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct., 14 (2003), 7-18.
- [12] R. M. El-Ashwah and M. K. Aouf, Differential subordination and superordination for certain subclasses of p−valent functions, Math. Comput. Modelling, 51(2010), 349-360.
- [13] Yu. E. Hohlov, Operators and operations in the univalent functions, Izv. Vyssh. Ucebn. Zaved. Mat., 10 (1978), 83-89 ( in Russian).
- [14] R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16 (1965), 755-658.
- [15] A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer. Math. Soc., 17 (1966), 352-357.
- [16] S. S. Miller and P. T. Mocanu, Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York and Basel, 2000.
- [17] S. S. Miller and P. T. Mocanu, Subordinates of differential superordinations, Complex Variables, 48 (2003), no. 10, 815-826.
- [18] V. O. Nechita, Differential subordinations and superordinations for analytic functions defined by the generalized S˘al˘agean derivative, Acta Univ. Apulensis, 16(2008), 143-156.
- [19] S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057-1077.
- [20] St. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Sco., 49 (1975), 109-115.
- [21] H. Saitoh, A linear operator and its applications of fiest order differential subordinations, Math. Japon. 44 (1996), 31-38.
- [22] G. S. Salagean, Subclasses of univalent functions, Lecture Notes in Math. (Springer-Verlag) 1013 , (1983), 362 - 372 .
- [23] C. Selvaraj and K. R. Karthikeyan, Differential subordination and superordination for certain subclasses of analytic functions, Far East J. Math. Sci. (FJMS), 29 (2008), no. 2, 419-430.
- [24] T. N. Shanmugam, V. Ravichandran and S. Sivasubramanian, Differantial sandwich theorems for some subclasses of analytic functions, J. Austr.Math. Anal. Appl., 3 (2006), no. 1, Art. 8, 1-11.
- [25] N. Tuneski, On certain sufficient conditions for starlikeness, Internat. J. Math. Math. Sci., 23 (2000), no. 8, 521-527.
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Bibliografia
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