International Journal of Nonlinear Analysis and Applications

Some differential subordinations and superordinations results for analytic univalent functions using Theyab-Atshan-Lupas-Abdullah operator

Document Type : Research Paper

Authors

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

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

Abstract

In this paper, we consider some differential subordinations and superordinations results for univalent functions by using the operator $(H_{\sigma,\rho,\tau,\mu,y,n})$ Also, we introduce 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] 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.
[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 (2021), no. 7, 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 (2021), no. 3, 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 (2009), no. 2, 11.
[10] T. Bulboaca, Classes of first–order differential superordinations, Demonst. Math. 35 (2002), no. 2, 287–292.
[11] T. Bulboaca, Differential subordinations and superordinations, recent results, House of Scientific Book Pub. Cluj-Napoca, 2005.
[12] I.A. Kadum, W.G. Atshan and A.T. Hameed, Sandwich theorems for a new class of complete homogeneous symmetric functions by using cyclic operator, Symmetry, 14 (2022), no. 10, 2223.
[13] 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.
[14] S.S. Miller and P.T. Mocanu, Differential subordinations: theory and applications, CRC Press, 2000.
[15] S.S. Miller and P.T. Mocanu, Subordinants of differential superordinations, Complex Variables 48 (2003), no. 10, 815–826.
[16] 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, p. 931.
[17] 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.
[18] T.N. Shanmugam, S. Shivasubramaniam and H. Silverman, On sandwich theorems for classes of analytic functions, Int. J. Math. Sci. 2006 (2006), no. 029684, 1–13.
[19] 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.
[20] S.D. Theyab, W.G. Atshan, A.A. Lupas and H.K. Abdullah, New results on higher-order differential subordination and superordination for univalent analytic functions using a new operator, Symmetry 14 (2022), no. 8, 1576.
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 8
August 2023
Pages 45-54
  • Receive Date: 22 October 2022
  • Revise Date: 13 February 2023
  • Accept Date: 18 February 2023