Articles

STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR

  • Samaneh Gholizadeh HAMIDI ,
  • Suzeini Abdul HALIM ,
  • Janusz SOKóL
Expand
  • Institute of Mathematical Sciences, Faculty of Science, University Malaya, 50603 Kuala Lumpur, Malaysia; Department of Mathematics, Rzesz´ow University of Technology, Al. Powsta´nc´ow Warszawy 12, 35-959 Rzesz´ow, Poland

Received date: 2013-04-15

  Revised date: 2014-04-15

  Online published: 2014-09-20

Abstract

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator Lαk . For functions in this class Hαk (pλ; h) we estimate the coefficients. Furthermore, some subordination properties related to the operator Lαk are also derived.

Cite this article

Samaneh Gholizadeh HAMIDI , Suzeini Abdul HALIM , Janusz SOKóL . STARLIKENESS AND SUBORDINATION PROPERTIES OF A LINEAR OPERATOR[J]. Acta mathematica scientia, Series B, 2014 , 34(5) : 1446 -1460 . DOI: 10.1016/S0252-9602(14)60095-3

References

[1] Bulboaca T. Differential Superordinations and Superordinations, Recent Results. Cluj-Napoca: House of Scientific Book Publ, 2005

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

[3] Miller S S, Mocanu P T. Differential subordinations and univalent functions. Michigan Math J, 1981, 28(2): 157–172

[4] Sok´o l J. A linear operator and associated class of multivalent analytic functions. Demonstratio Math, 2007, 40(3): 559–566

[5] Dziok J, Srivastava H M. Classes of analytic functions associated with the generalized hypergeometric function. Appl Math Comput, 1999, 103(1): 1–13

[6] Dziok J, Srivastava H M. Some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function. Adv Stud Contemp Math (Kyungshang), 2002, 5(2): 115–125

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

[8] Liu J L. Strongly starlike functions associated with the Dziok-Srivastava operator. Tamkang J Math, 2004, 35(1): 37–42

[9] Aouf M K, Dziok J. Distortion and convolutional theorems for operators of generalized fractional calculus involving Wright function. J Appl Anal, 2008, 14(2): 183–192

[10] Carlson B C, Shaffer D B. Starlike and prestarlike hypergeometric functions. SIAM J Math Anal, 1984, 15(4):737–745

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

[12] Piejko K, Sok´o l J. Subclasses of meromorphic functions associated with the Cho-Kwon-Srivastava operator. J Math Anal Appl, 2008, 337(2): 1261–1266

[13] Patel J, Sahoo P. Properties of a class of multivalent analytic functions. Comput Math Appl, 2003,  46(10/11): 1633–1644

[14] Saitoh H. A linear operator and its applications of first order differential subordinations. Math Japon, 1996, 44(1):31–38

Outlines

/