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F. Ghanim



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F. Ghanim


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 16, 2017

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 16, 2017



Inclusion Properties for a Certain Class of Analytic Function Related to Linear Operator

AUTHORS: F. Ghanim

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ABSTRACT: In this paper, we introduce a new class of analytic functions defined by a new convolution operator Lαt(α,β). The new class of analytic functions Σα,βα,t (ρ;h) in U* = {z: 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates various properties of certain classes of meromorphically univalent functions

KEYWORDS: Analytic function, Convex function, Starlike function, Prestarlike function, Meromorphic function, Hurwitz Zeta function, Linear operator, Hadamard product


REFERENCES:

[1] S. G. Krantz, Meromorphic functions and singularities at infinity, Handbook of Complex Variables. , Boston, MA: Birkhuser (1999),pp. 63- 68.

[2] F. Ghanim, Properties for Classes of Analytic Function Related to Integral Operator, WSEAS TRANSACTIONS on MATHEMATICS 13 (2014),Art. 46, 477-483.

[3] F. Ghanim, Some Properties on a Certain Class of Hurwitz Zeta function Related To linear operator,16th International Conference on Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS ’14). 2014, 35-39.

[4] F. Ghanim, A study of a certain subclass of Hurwitz-Lerch-Zeta function related to a linear operator, Abstract and Applied Analysis, Online article (2013), http://www.hindawi.com /journals/aaa/2013/763756/abs/.

[5] A. W. Goodman, Functions typically-real and meromorphic in the unit circle, Trans. Amer. Math. Soc. 81 (1956), 92-105.

[6] H. M. Srivastava, S. Gaboury and F. Ghanim, Certain subclasses of meromorphically univalent functions defined by a linear operator associated with the λ-generalized Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct. (Accepted).

[7] H. M. Srivastava, S. Gaboury and F. Ghanim, A unified class of analytic functions involving a generalization of the Srivastava-Attiya operator, Applied Mathematics and Computation (Accepted).

[8] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwoord Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.

[9] H. M. Srivastava and A. A. Attiya, An integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination, Integral Transforms and Special Functions, 18(3), (2007), 207-216.

[10] H. M. Srivastava and J. Choi, Series associated with the Zeta and related functions, Kluwer Academic Publishers, (2001).

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[12] H. M. Srivastava, R. K. Saxena, T. K. Pogany, and R. Saxena, Integral transforms and special functions, Appl. Math. Comput., 22 (7), (2011), 487-506.

[13] J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (1) (2003), 7-18.

[14] F. Ghanim and M. Darus,, New Subclass of Multivalent Hypergeometric Meromorphic Functions, , International J. of Pure and Appl. Math., 61 (3) (2010), 269-280.

[15] F. Ghanim and M. Darus, New result of analytic functions related to Hurwitz-Zeta function, The Scientific World Journal, vol. 2013, Article ID 475643, 5 pages, 2013. doi:10.1155/2013/475643.

[16] J. L. Liu and H. M. Srivastava, Certain properties of the Dziok-Srivastava operator, Appl. Math. Comput., 159, (2004), 485-493.

[17] J. L. Liu and H.M. Srivastava, Classes of meromorphically multivalent functions associated with the generalized hypergeometric function , Math. Comput. Modelling, 39 (1) (2004),21-34.

[18] S.S. Miller, P.T. Mocanu, Differential subordinations and univalent functions, Michigan Math.J., 28(1981), 157-171.

[19] St. Ruscheweyh, Convolutions in Geometric Function Theory, Sem. Math. Sup. 83, Presses Univ. Montreal 1982.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 16, 2017, Art. #32, pp. 283-289


Copyright © 2017 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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