Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 16 (2021), 1 -- 11

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

SUBORDINATING RESULTS FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY HADAMARD PRODUCT AND ATSHAN AND RAFID OPERATOR

M. K. Aouf, A. O. Mostafa and F. Y. Al-Quhali

Abstract. In this paper, we defined a class of analytic functions defined by Hadamard product and Atshan and Rafid operator and obtained some subordinating results for functions in this class.

2020 Mathematics Subject Classification: 30C45
Keywords: Analytic function; Hadamard product; Atshan and Rafid operator; subordinating; factor sequence.

Full text

References

  1. M. K. Aouf and A. O. Mostafa, Some subordination results for certain classes of analytic functions defined by the Al-Oboudi-Al-Amoudi operator, Arch. Math., 29(2009), 279-286. MR2496680. Zbl 1165.30313.

  2. M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Subordination theorem of analytic functions defined by convolution, Complex Anal. Oper. Theory, (4)(2013), 1117-1126. Zbl 1356.30006.

  3. M. K. Aouf, A. Shamandy, A. O. Mostafa and E. A. Adwan, Subordination results for certain class of analytic functions defined by convolution, Rend. Cire. Mat., 60(2011), 255-262. Zbl 1231.30003.

  4. W. G. Atshan and H. B. Rafid, Fractional calculus of a class of univalent functions with negative coefficients defined by Hadamard product with Rafid-operator, European J. Pure Appl. Math., 4(2) (2011), 165-173. Zbl 1389.30031.

  5. S. D. Bernardi, Convex and starlike univalent functions, Trans. American Math. Soc., 135(1969), 429-449. MR0232920. Zbl 0172.09703.

  6. B. C. Carlson and D. B. Shffer, Starlike and prestarlike hypergeometric functions, J. Math. Anal. Appl., 15(1984), 737-745. MR747433. Zbl 0567.30009.

  7. A. Catas, G. I. Oros and G. Oros, Differential subordinations associated with multiplier transformations, Abstr. Appl. Anal., (ID 845724) 2008(2008), 1-11. Zbl 1153.30021.

  8. N. E. Cho, O. S. Kwon and H. M. Srivastava, Inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators, J. Math. Anal. Appl., 292(2004), 470-483. Zbl 1059.30006.

  9. J. H. Choi, M. Saigo and H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276(2002), 432-445. MR1944360. Zbl 1035.30004.

  10. J. Dziok and H. M. Srivastava, Classes of analytic functions with the generalized hypergeometric function, Appl. Math. Comput., 103(1999), 1-13. MR1686354. Zbl 0937.30010.

  11. J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transform. Spec. Funct., 14(2003), 7-18. MR1949212. Zbl 1040.30003.

  12. R. J. Libera, Some classes of regular univalent functions, Proc. American Math. Soc., 16(1969), 755-758. MR0178131. Zbl 0158.07702.

  13. A. E. Livingston, On the radius of univalent of certain analytic functions, Proc. American Math. Soc., 17(1966), 352-357. MR0188423. Zbl 0158.07701.

  14. S. S. Miller and P. T. Mocanu, Differential Subordination: Theory and Applications, CRC Press, New York, 2000.

  15. J. Nishiwaki and S. Owa, Coefficient inequalities for certain analytic functions, Int. J. Math. Sci., 29(5) (2002), 285-290. Zbl 1003.30006.

  16. K. I. Noor, On new classes of integral operator, J. Nat. Geom., 16(1999), 71-80. Zbl 0942.30007.

  17. S. Owa and J. Nishiwaki, Coefficient estimates for certain classes of analytic functions, J. Inequal. Pure Appl. Math., 3(5) (2002), 1-12. Zbl 1033.30013.

  18. S. Owa and H. M. Srivastava, Some generalized convolution properties associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math., 3(3) (2002), 1-27. Zbl 0999.30017.

  19. S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canda J. Math., 39(1987), 1057-1077. MR918587. Zbl 0611.33007.

  20. St. Ruscheweyh, New criteria for univalent functions, Proc. American Math. Soc., 49(1975), 109-115. MR0367176. Zbl 0303.30006.

  21. H. M. Srivastava and A. A. Attiya, Some subordination results associated with certain subclasses of analytic functions, J. Inequal. Pure Appl. Math. 5(4), 82(2004), 1-14. Zbl 1059.30021.

  22. S. Wilf, Subordinating factor sequence for convex maps of the unit circle, Proc. American Math. Soc., 12(1961), 689-693. MR0125214. Zbl 0100.07201.



M. K. Aouf
Mansoura University
Department of Mathematics,
35516, Mansoura, Egypt.
e-mail: mkaouf127@yahoo.com

A. O. Mostafa
Mansoura University
Department of Mathematics,
35516, Mansoura, Egypt.
e-mail: adelaeg254@yahoo.com

F. Y. Al-Quhali
Mansoura University
Department of Mathematics,
35516, Mansoura, Egypt.
e-mail: fyalquhali89@gmail.com



http://www.utgjiu.ro/math/sma