Certain Classes of Meromorphic p-Valent Functions Associated with Mittag-Leffler Function
Certain Classes of Meromorphic p-Valent Functions
DOI:
https://doi.org/10.53560/PPASA(58-1)536Keywords:
Differential Subordination, Mittag-Leffler Function, Meromorphic p-valent Functions, 2010 Mathematics Subject Classification: 30C45Abstract
In this paper, using definition of subordination and Mittag-Leffler function we introduce classes of p-valent meromorphic functions and obtain some subordination results for these classes.
References
S.S. Miller & P.T. Mocanu. Differential Subordination Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker, New York and Basel (2000).
T. Bulboacă. Differential Subordinations and Superordinations. New Results, House of Scientific Book Publ., Cluj-Napoca. ISBN 973-686-777-3 (2005).
G. M. Mittag-Leffler. Sur la nouvelle function , C. R. Acad. Sci. Paris, 137, 554-558 (1903).
A. Wiman. Über den Fundamental satz in der Theorie der Funcktionen , Acta Math., 29, 191-201 (1905).
A. Wiman. Über die Nullstellun der Funcktionen , Acta Math., 29, 217-134 (1905).
H. M. Srivastava & Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math. Comp., 211, 198-210 (2009).
A. O. Mostafa, & M.K. Aouf, Some inequalities for meromorphic multivalent functions associated with Mittag-Leffler function, Int. J. Open Problems Complex Analysis, vol. 10, no. 1, 1-8 (2018).
R. M. El-Ashwah, A note on certain meromorphic p-valent functions, Appl. Math. Letters, 22 , 1756-1759 (2009).
M. K. Aouf, A. Shamandy, A.O. Mostafa & S. M. Madian. Properties of some families of meromorphic p-valent functions involving certain differential operator, Acta Univ. Apulensis, 20 , 7-16 (2009).
R. M. El-Ashwah, & M. K. Aouf. Some properties of certain subclasses of meromorphically p-valent functions involving extended multiplier transformations, Comput. Math. Appl., 59 , 2111-2120 (2010).
F. M. Al-Oboudi, & H. A. Al-Zkeri. Applications of Briot Bouquet differential subordination to certain classes of meromorphic functions, Arab J. Math. Sci.,12 , 1-14 (2005).
M.K. Aouf & H.M. Hossen. New certeria for meromorphic p-valent starlike functions, Tsukuba J. Math., 17 , no. 2, 481-486 (1993).
D. J. Hallenbeck & St. Ruscheweyh. Subordination by convex function, Proc. Amer. Math. Soc., 52 ,191-195 (1975).
E. T. Whittaker & G. N. Watson. 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, Gourth Edition, Cambridge University Press, Cambridge, (1927).
D. Pashkouleva, The starlikeness and spiral-convexity of analytic function , in : H. M. Srivastava and S. Owa (Editors), Current Topics in Analytic Function Theory, pp. 266-273, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, (1992).
J. Stankiewicz & Z. Stankiewicz. Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie- Sklodowska Sect. A, 40, 251-265 (1986).