Sandwich results for higher order fractional derivative operators |
|
Author |
hanaa_zayed42@yahoo.com1, bulboaca@math.ubbcluj.ro2
1) Department of Mathematics, Faculty of Science
Menofia University, Shebin Elkom, Egypt; 2) Faculty of Mathematics and Computer Science
Babes-Bolyai University, Cluj-Napoca, Romania
|
Abstract |
In this paper we obtain some differential subordinations and superordinations related to
a generalized fractional derivative operator for higher order derivatives of multivalent functions.
Moreover, we derive some sandwich results under certain assumptions on the parameters
involved, and these new results generalize some previously well-known theorems.
|
Keywords |
analytic functions; univalent functions; differential subordination and superordination; hypergeometric
function; generalized fractional derivative operator
|
DOI |
doi:10.15330/ms.49.1.52-66
|
Reference |
1. R.M. Ali, V. Ravichandran, K.M. Hussain, K.G. Subramanian, Differential sandwich theorems for certain
analytic functions, Far East J. Math. Sci., 15 (2004), №1, 87-94.
2. S.M. Amsheri, V. Zharkova, Differential subordinations and superordinations for p-valent functions defined by fractional derivative operator, Demonstr. Math., 46 (2013), №3, 505-515. 3. S.M. Amsheri, V. Zharkova, Differential sandwich theorems of p-valent functions associated with a certain fractional derivative operator, Kragujevac J. Math., 35 (2011), №3, 387-398. 4. M.K. Aouf, A.O. Mostafa, H.M. Zayed, Some characterizations of integral operators associated with certain classes of p-valent functions defined by the Srivastava-Saigo-Owa fractional differintegral operator, Complex Anal. Oper. Theory, 10 (2016), №6, 1267-1275. 5. M.K. Aouf, A.O. Mostafa, H.M. Zayed, Subordination and superordination properties of p-valent functions defined by a generalized fractional differintegral operator, Quaest. Math., 39 (2016) №4, 545-560. 6. M.K. Aouf, A.O. Mostafa, H.M. Zayed, On certain subclasses of multivalent functions defined by a generalized fractional differintegral operator, Afr. Mat., 28 (2017), №1-2, 99-107. 7. T. Bulboaca, Classes of first-order differential superordinations, Demonstr. Math., 35 (2002), №2, 287-292. 8. T. Bulboaca, A class of superordination-preserving integral operators, Indag. Math. (N.S.), 13 (2002), №3, 301-311. 9. T. Bulboaca, Differential subordinations and superordinations, new results, House of Scientific Boook Publ., Cluj-Napoca, 2005. 10. G.P. Goyal, J.K. Prajapat, A new class of analytic p-valent functions with negative coefficients and fractional calculus operators, Tamsui Oxf. J. Inf. Math. Sci., 20 (2004), №2, 175-186. 11. S.S. Miller, P.T. Mocanu, Differential subordinations: theory and applications, Series on Monographs and Textbooks in Pure and Appl. Math., V.255, Marcel Dekker, Inc., New York, 2000. 12. S.S. Miller, P.T. Mocanu, Subordinations of differential superordinations, Complex Var., 48 (2003) №10, 815-826. 13. A.O. Mostafa, M.K. Aouf, H.M. Zayed, T. Bulboac.a, Multivalent functions associated with Srivastava- Saigo-Owa fractional differintegral operator. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, https://doi.org/10.1007/s13398-017-0436-1, /to appear/ 14. S. Owa, On the distortion theorems I. Kyungpook Math. J., 18 (1978), 53-59. 15. W.C. Royster, On the univalence of a certain integral, Michigan Math. J., 12 (1965), №4, 385-387. 16. T.N. Shanmugam, V. Ravichandran, S. Sivasubramanian, Differential sandwich theorems for some subclasses of analytic functions, Aust. J. Math. Anal. Appl., 3 (2006), №1, 1-11. |
Pages |
52-66
|
Volume |
49
|
Issue |
1
|
Year |
2018
|
Journal |
Matematychni Studii
|
Full text of paper | |
Table of content of issue |