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SOME SUBORDINATION PROPERTIES OF THE LINEAR OPERATOR
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 Title & Authors
SOME SUBORDINATION PROPERTIES OF THE LINEAR OPERATOR
PANIGRAHI, TRAILOKYA;
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 Abstract
In this paper, subordination results of analytic function involving linear operator are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator are investigated.
 Keywords
multivalent functions;differential subordination;Komatu integral operator;Gauss hypergeometric function;
 Language
English
 Cited by
 References
1.
S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446. crossref(new window)

2.
A. Ebadian and S. Najafzadeh, Uniformly starlike and convex univalent functions by using certain integral operator, Acta Univ. Apulensis Math. Inform. 20 (2009), 17-23.

3.
A. Ebadian, S. Shams, Z. G.Wang, and Y. Sun, A class of multivalent analytic functions involving the generalized Jung-Kim-Srivastava operator, Acta Univ. Apulensis Math. Inform. 18 (2009), 265-277.

4.
D. J. Hallenbeck and St. Ruscheweyh, Subordination by convex functions, Proc. Amer. Math. Soc. 52 (1995), 191-195.

5.
S. M. Khairnar and M. More, On a subclass of multivalent uniformly starlike and convex functions defined by a linear operator, IAENG Int. J. Appl. Math. 39 (2009), no. 3, 175-183.

6.
Y. Komatu, On analytic prolongation of a family of operators, Mathematica (Cluj) 32(55) (1990), no. 2, 141-145.

7.
S. S. Miller and P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28 (1981), no. 2, 157-171. crossref(new window)

8.
S. S. Miller, Differential Subordinations: Theory and Applications, in: Monographs and Textbooks in Pure and Applied Mathematics, 225, Marcel Dekker, New York, 2000.

9.
R. K. Raina and I. B. Bapna, On the starlikeness and convexity of a certain integral operator, Southeast Asian Bull. Math. 33 (2009), no. 1, 101-108.

10.
T. O. Salim, A class of multivalent functions involving a generalized linear operator and subordination, Int. J. Open Problems Complex Analysis 2 (2010), no. 2, 82-94.

11.
S. Shams, S. R. Kulkarni, and J. M. Jahangiri, Subordination properties of p-valent functions defined by integral operators, Int. J. Math. Math. Sci. 2006 (2006), Article ID 94572, 1-3.

12.
H. M. Srivastava and S. Owa (Eds.), Current Topics in Analytic Function Theory, World Scientific, Singapore, 1992.

13.
J. Stankiewicz and Z. Stankiewicz, Some applications of the Hadamard convolution in the theory of functions, Ann. Univ. Mariae Curie-Sklodowska Sect. A 40 (1986), 251- 265.

14.
S. R. Swamy, Some subordination properties of multivalent functions defined by certain linear operators, J. Math. Comput. Sci. 3 (2013), no. 2, 554-568.

15.
E. T. Whittaker and G. N. Watson, A Course on Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions, with an Account to the Principle Transcendental Functions, 4th Edition, Cambridge University Press, Cambridge, 1927.