Subordination for multivalent analytic functions associated with Wright generalized hypergeometric function.

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PDF Subordinations for multivalent analytic functions associated with Wright generalized hypergeometric function Subordinations for multivalent analytic functions associated with Wright generalized hypergeometric function
Published: Mar 30, 2013
DOI: https://doi.org/10.5556/j.tkjm.44.2013.1009
Keywords:
Dziok--Srivastava operator, Dziok--Raina operator, Hadamard product, univalent functions, $p$--valent functions, convolution, differential subordination.

Main Article Content

J. Sokol
N. Sarkar
P. Goswami
J. Dziok

Abstract

Recently M. K. Aouf and T. M. Seoudy, (2011, {\it Integral Trans. Spec. Func.} {\bf 22}(6) (2011), 423--430) have introduced families of analytic functions associated with the Dziok--Srivastava operator. In this work we use the Dziok--Raina operator to consider classes of multivalent analytic functions. It is connected with Wright generalized hypergeometric function, see J. Dziok and R. K. Raina (2004, {\it Demonstratio Math.}, {\bf 37}(3) 533--542). Moreover, we present a new result which extends some of the earlier results and give other properties of these classes. We have made use of differential subordinations and properties of convolution in geometric function theory.

Article Details

How to Cite
Sokol, J., Sarkar, N., Goswami, P., & Dziok, J. (2013). Subordination for multivalent analytic functions associated with Wright generalized hypergeometric function. Tamkang Journal of Mathematics, 44(1), 61–71. https://doi.org/10.5556/j.tkjm.44.2013.1009
Issue
Vol. 44 No. 1 (2013)
Section
Papers
Author Biographies

J. Sokol

Department of Mathematics, Rzeszów University of Technology, Al. Powsta´nców Warszawy 12, 35-959 Rzeszów, Poland.

N. Sarkar

Department ofMathematics, Jadavpur University, Kolkata-700032, India.

P. Goswami

Department ofMathematics, AMITY University Rajasthan, Jaipur-302002, India.

J. Dziok

Institute ofMathematics, University of Rzeszów, Rejtana 16A, 35-310 Rzeszów, Poland.

References

M. K. Aouf and T. M. Seoudy, Classes of analytic functions related to the Dziok--Srivastava operator, Integral Trans. Spec. Func., 22(2011), 423--430.

S. K. Bansal, J. Dziok and P. Goswami, Certain results for a subclass of meromorphic multivalent functions associated with the Wright function, Europian J. Pure Appl. Math., 3(2010), 633--640.

I. W. Rabha and M. Darus,New classes of analytic functions involving generalized noor integral operator, Journal of Inequalities and Applications,2008(2008), Article ID 390435.

J. Dziok, Applications of extreme points to distortion estimates, App. Math. Comput., 215 (2009), 71--77.

J. Dziok and H. M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1--13.

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

J. Dziok and R. K. Raina, Families of analytic functions associated with the Wright generalized hypergeometric function, Demonstratio Math.,37(2004), 533--542.

J. Dziok and R. K. Raina, Some results based on first order differential subordination with the Wright's generalized hypergeometric function, Comment. Math. Univ. St. Pauli, 58(2009), 87--94.

J. Dziok, R. K. Raina and H. M. Srivastava, Some classes of analytic functions associated with operators on Hilbert space involving Wright generalized hypergeometric function, Proc. Jangieon Math. Soc., 7(2004), 43--55.

P. J. Eenigenburg, S. S. Miller and P. T. Mocanu and O. M. Reade, Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65(1978),

--305.

S. S. Miller and P. T. Mocanu, Differential Subordinations: Theory and Applications, Series of Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker,Inc., New York Basel (2000).

R. K. Raina and T. S. Nahar, A note on boundedness properties of Wright generalized hypergeometric function, Ann. Math. Blaise Pascal, 4 (1997), 83--95.

R. K. Raina and T. S. Nahar, On characterization of certain Wright generalized hypergeometric functions involving certain subclasses of analytic functions, Informatica, 10(1999), 219--230.

S. Sivasubramanian and J. Sokol, Hypergeometric transforms in certain classes of analytic functions, Mathematical and Computer Modelling, 54(2011), 3076--3082.

J. Sokol, On some applications of the Dziok-Srivastava operator, Appl. Math. Comput., 201(2008),774--780.

E. M. Wright, The asymptotic expansion of the generalized Hypergeometric function, Proc. London. Math. Soc., 46 (1946), 389--408.