Differential subordinations and superordinations result for analytic univalent functions using the Darus-Faisal operator

Document Type : Research Paper

Authors

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

Abstract

In this paper, we introduce some differential subordinations and superordinations results for a subclass of analytic univalent functions in the open unit disk $U$ using the Darus-Faisal operator $G^{m}_{\lambda} (\sigma,\delta,\tau)$. Also, we study some sandwich theorems.

Keywords

[1] R. Abd Al-Sajjad and W.G. Atshan, Certain analytic function sandwich theorems involving operator defined by Mittag-Leffler function, AIP Conf. Proc. 2398 (2022), 060065.
[2] 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 (2020), no. 4, 803–809.
[3] 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.
[4] 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.
[5] 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(2006), no. 1, 17–30.
[6] W.G. Atshan and A.A.R. Ali, On some sandwich theorems of analytic functions involving Noor-Salagean operator, Adv. Math.: Sci. J. 9 (2020), no. 10, 8455–8467.
[7] W.G. Atshan and A.A.R. Ali, On sandwich theorems results for certain univalent functions defined by generalized operators, Iraqi J. Sci. 62 (2021), no. 7, 2376–2383.
[8] 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 (2021), no. 3, 579–591.
[9] 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.
[10] 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 (2009), no. 2, 11.
[11] 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 (2021), no. 9, 1653.
[12] T. Bulboaca, Classes of first–order differential superordinations, Demonst. Math. 35 (2002), no. 2, 287–292.
[13] T. Bulboaca, Differential subordinations and superordinations, recent results, House of Scientific Book Publ. Cluj-Napoca, 2005.
[14] M. Darus, and I. Faisal, A different approach to normalized analytic functions through meromorphic functions defined by extended multiplier transformations operator, Int. J. App. Math. Stat. 23 (2011), no. 11, 112–121.
[15] I.A. Kadum, W.G. Atshan and A.T. Hameed, Sandwich theorems for a new class of complete homogeneous symmetry, functions by using cyclic operator, Symmetry 14 (2022), no. 10, 2223.
[16] B.K. Mihsin, W.G. Atshan and S.S. Alhily, On new sandwich results of univalent functions defined by a linear operator, Iraqi J. Sci. 63 (2022), no. 12, 5467–5475.
[17] 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.
[18] S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Variables 48 (2003), no. 10, 815–826.
[19] M.A. Sabri, W.G. Atshan and E. El-Seidy, On sandwich-type results for a subclass of certain univalent functions using a new Hadamard product operator, Symmetry 14 (2022), no. 5, 931.
[20] F.O. Salman and W.G. Atshan, New results on integral operator for a subclass of analytic functions using differential subordinations and superordinations, Symmetry 15 (2023), no. 2, 1–10.
[21] T.N. Shanmugam, S. Shivasubramaniam and H. Silverman, On sandwich theorems for classes of analytic functions, Int. J. Math. Sci. 29684 (2006), 1–13.
[22] S.D. Theyab, W.G. Atshan and H.K. Abdullah, On some sandwich results of univalent functions related by differential operator, Iraqi J. Sci. 63 (2022), no. 11, 4928–4936.
Volume 14, Issue 11
November 2023
Pages 53-61
  • Receive Date: 17 December 2022
  • Revise Date: 08 February 2023
  • Accept Date: 03 March 2023