Certain Class of Meromorphic Univalent Functions Defined by an Erdelyi-Kober Type Integral Operator
[1]
R. M. El-Ashwah, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt.
In this paper, we investigate interesting subordination properties for certain subclasses of meromorphic analytic and univalent functions in the puncture unit disc which are defined here by means of new linear operator. Further, few interesting special cases and examples are obtained for an appropriate choices of the parameters and the corresponding functions.
Meromorphic Function, Convex Function, Convolution, Differential Subordination
[1]
F. M. Al-Oboudi and H. A. Al-Zkeri, Applications of Briot-Bouquet differential subordination to certain classes of meromorphic functions, Arab J. Math. Sci., 12(2005), no. 1, 1-14.
[2]
E. Aqlan, J. M. Jahangiri and S. R. Kulkarni, Certain integral operators applied to meromorphic p-valent functions, J. Nat. Geom., 24(2003), 111-120.
[3]
T. Bulboacă, Integral operators that preserve the subordination, Bull. Korean Math. Soc., 34(1997), no. 4, 627--636
[4]
N. E. Cho, O. S. Kwon and H. M Srivastava, Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl., 300(2004), 505-520.
[5]
N. E. Cho, O. S. Known and H. M. Srivastava, Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations, Integral Transforms Special Functions, 16(2005), no. 18, 647-659.
[6]
R. M. El-Ashwah, A note on certain meromorphic p-valent functions, Appl. Math. Letters, 22 (2009), 1756-1759.
[7]
R. M. El-Ashwah, Properties of certain class of p-valent meromorphic functions associated with new integral operator, Acta Universitatis Apulensis, (2012), no. 29, 255-264.
[8]
V. Kiryakova, gGeneralization fractional calculus and applications, Pitman Research Note in Math. Series, 301, John Willey& sons, Inc. new york, 1994.
[9]
A. Y. Lashin, On certain subclass of meromorphic functions associated with certain integral operators, Comput. Math Appl., 59(2010), no.1, 524-531.
[10]
T. H. Gronwall, Some remarks on conformal representation, Ann. Math., 16(1914/15), 72--76.
[11]
S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J., 28(1981), 157--171
[12]
S. S. Miller and P. T. Mocanu, Univalent solutions of Briot-Bouquet differential equations, J. Differential Equations, 56(1985), 297--309
[13]
S. S. Miller and P. T. Mocanu, Differential Subordinations. Theory and Applications, Marcel Dekker, New York, 1999
[14]
S. S. Miller and P. T. Mocanu, Subordinants of differential superordinations, Complex Variables, 48(10)(2003), 815--826
[15]
S. S. Miller, P. T. Mocanu and M. O. Reade, Subordination preserving integral operators, Trans. Amer. Math. Soc., 283(1984), 605--615
[16]
S. Owa and H. M. Srivastava, Some subordination theorems involving a certain family of integral operators, Integral Transforms Spec. Funct., 15(2004), 445--454
[17]
Ch. Pommerenke, Univalent Functions, Vanderhoeck and Ruprecht, Göttingen, 1975.
[18]
B. A. Uralegaddi and C. Somanatha, New criteria for meromorphicstarlike univalent functions, Bull. Austral.Math. Soc., 43 (1991), 137-140.
