Some sandwich theorems for meromorphic univalent functions defined by Hadamard product of integral operators

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Science, University of Al-Qadisiyah, Al-Diwaniyah, Iraq

2 Department of Mathematics, College of Education for Girls, University of Kufa, Najaf, Iraq

Abstract

In the present paper, we obtain some subordination and superordination results, involving the operator Ta for functions of the form f(z)=z1+k=1akzk, which are meromorphic univalent in the punctured open unit disk these results are applied to obtain sandwich results.

Keywords

[1] S.A. Al-Ameedee, W.G. Atshan and F.A. Al-Maamori, On sandwich results of univalent functions defined by a
linear operator, J. Interdiscip. Math. 23(4) (2020) 803–809.
[2] S.A. Al-Ameedee, W.G. Atshan and F.A. Al-Maamori, Some new results of differential subordinations for higherorder derivatives of multivalent functions, J. Phys.: Conf. Ser. 1804 (2021) 012111.
[3] R.M. Ali, V. Ravichandran, M.H. Khan and K.G. Subramanian, Differential sandwich theorems for certain
analytic functions, Far East J. Math. Sci. 15 (2004) 87–94.
[4] F.M. Al-Oboudi and H.A. Al-Zkeri, Applications of Briot-Bouquet differential subordination to some classes of
meromorphic functions, Arab J. Math. Sci. 12(1) (2006) 17–30.
[5] W.G. Atshan and A.A.R. Ali, On some sandwich theorems of analytic functions involving Noor-Saˇlaˇgean operator,
Adv. Math.: Sci. J. 9(10) (2020) , 8455–8467.
[6] W.G. Atshan and A.A.R. Ali, On sandwich theorems results for certain univalent functions defined by generalized
operators, Iraqi J. Sci. 62(7) (2021) 2376–2383.
[7] W.G. Atshan, A.H. Battor and A.F. Abaas, Some sandwich theorems for meromorphic univalent functions defined
by new integral operator, J. Interdiscip.Math. 24(3) (2021) 579–591.
[8] W.G. Atshan and R.A. Hadi, Some differential subordination and superordination results of p-valent functions
defined by differential operator, J. Phys.: Conf. Ser. 1664 (2020) 012043.
[9] W.G. Atshan and S.R. Kulkarni, On application of differential subordination for certain subclass of Meromorphically p-valent functions with positive coefficients defined by linear operator, J. Inequal. Pure Appl. Math. 10(2)
(2009).
[10] W.G. Atshan, I.A.R. Rahman and A.A. Lupas, Some results of new subclasses for bi-univalent functions using
quasi-subordination, Symmetry 13(9) (2021) 1653.
[11] T. Bulboacˇa, Classes of first-order differential superordinations, Demonstration Math. 35(2) (2002) 287–292.
[12] T. Bulboacˇa, Differential subordinations and superordinations, Recent Results, House of Scientific Book Publ.
Cluj-Napoca, 2005.
[13] R.M. El-Ashwah and M.K. Aouf, Differential subordination and superordination for certain subclasses of p-valent
functions, Math. Comput. Model. 51(5-6) (2010) 349–360.
[14] A.Y. Lashin, On certain subclass of meromorphic functions associated with certain integral operators, Comput.
Math. Appl. 59 (2010) 524–531.
[15] S.S. Miller and P.T. Mocanu, Differential subordinations: Theory and applications, Series on Monographs and
Textbooks in Pure and Applied Mathematics, Marcel Dekker Inc. New York and Basel, 2000.
[16] S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Var. 48(10) (2003) 815–826.
[17] T.N. Shanmugam, S. Shivasubramaniam and H. Silverman, On sandwich theorems for classes of analytic functions, Int. J. Math. Sci. 2006 (2006) 1–13.
Volume 12, Special Issue
December 2021
Pages 2403-2412
  • Receive Date: 13 October 2021
  • Revise Date: 10 November 2021
  • Accept Date: 07 December 2021