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Certain Subclass of P-valent Meromorphic Functions Involving the Extended Multiplier Transformations
Current Issue
Volume 3, 2015
Issue 3 (June)
Pages: 43-49   |   Vol. 3, No. 3, June 2015   |   Follow on         
Paper in PDF Downloads: 37   Since Aug. 28, 2015 Views: 1992   Since Aug. 28, 2015
Authors
[1]
R. M. El-Ashwah, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, Egypt.
Abstract
Using the linear operator I_p^m (λ,l)(λ≥0,l>0,p∈N,m∈N_0=N∪{0}) for a function f(z)∈∑_p the class of P-valent meromorphic functions El-Ashwah [6] and the principle of subordination [11], we introduce the class M_(p,k)^m (λ,l;β;ϕ), which satisfies the following condition: 1/(β-p) [β+z(I_p^m (λ,l)f(z))'/(f_(p,k)^m (λ,l;z) )]<ϕ(z) (β>p;ϕ∈p;z∈U). Such results as inclusion relationships, integral representations, convolution properties and integral-preserving properties for these functions class are obtained.
Keywords
Subordination, Analytic, Meromorphic, Multivalent, Multiplier Transformations
Reference
[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]
M. K. Aouf and H. M. Hossen, New criteria for meromorphic p-valent starlike functions, Tsukuba J. Math., 17(1993), 481-486.
[3]
N. E. Cho, O. S. Kwon, and H. M Srivastava, Inclusion and argument propertie for certain subclasses of meromorphic functions associated with a family of multiplier transformations, J. Math. Anal. Appl., 300(2004), 505-520.
[4]
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.
[5]
P. J. Eenigenburg, S. S. Miller, P. T. Mocanu and M. O. Reade, Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978), 289--305.
[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 and M. K. Aouf, Differential subordination and superordination on p-valent meromorphic functions defined by extended multiplier transformations, European J. Pure Appl. Math., 3(2010), no. 6, 1070-1085
[8]
R. M. El-Ashwah and M. K. Aouf, Some properties of certain subclasses of meromorphically p-valent functions involving extended multiplier transformations, Comput. Math. Appl. 59(2010), 2111-2120.
[9]
R. M. El-Ashwah, Properties of certain class of p-valent meromorphic functions associated with new integral operator, Acta Univ. Apulensis, (2012), no. 29, 255-264.
[10]
R. M. EL-Ashwah, M. K. Aouf and T. Bulboaca, Differential subordinations for classes of meromorphic p—valent Functions defined by multiplier transformations, Bull. Austr.Math. Soc., 83(2011), 353-368.
[11]
S. S. Miller and P. T. Mocanu, On some classes of first order differential subordination, Michigan Math. J. 32(1985), 185-195.
[12]
S. S. Miller and P. T. Mocanu, Differential Subordinations : Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math. no. 225, Marcel Dekker, Inc. New York, 2000.
[13]
K. S. Padmanabhan and R. Parvathem, Some applications of differential subordination, Bull. Austral. Math. Soc., 32(1985), 321-330.
[14]
S. M. Sarangi, and S. B. Uralegaddi, Extreme points of meromorphic univalent functions with two fixed points, Analels Stintifice Ale Univ., 11(1995), 127-134.
[15]
H. M. Srivastava and J. Patel, Applications of differential subordination to certain classes of meromorphically multivalent functions, J. Ineq. Pure Appl. Math., 6(2005), no. 3, Art.88, 1-15.
[16]
B. A. Uralegaddi and C. Somanatha, New criteria for meromorphic starlike univalent functions, Bull. Austral. Math. Soc., 43(1991), 137-140.
[17]
Z. Wang, Y, Sun and Z, Zhang, Certain classes meromorphic multivalent functions, Comput. Math. Appl., 58(2009), 1408-1417.
[18]
Z. Wang, Z. Liu and A. Catas, On neighborhood and partial sums of certain meromorphic multivalent functions, Appl. Math. Letters, 24(2011), 864-868.
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