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 $T^{a}$ for functions of the form $f(z)=z^{-1}+\sum_{k=1}^{\infty}a_k z^{k}$, 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