---

Discontinuity, Nonlinearity, and Complexity 10(2) (2021) 323--331 | DOI:10.5890/DNC.2021.06.011

Saba N. Al-khafaji , Ahmed Hadi Hussain, Sameer Annon Abbas

Department of Mathematics, Faculty of Computer Science and Mathematics, University of Kufa-Iraq

Download Full Text PDF

 

Abstract

The main object of this paper is to introduce a new class of Bazilevi\'{c} functions $\Omega^n_\alpha(m, \delta)$ in the open unit disk $\mathbb{D}$ associated with linear differential operator. In addition to, we obtained the coefficient estimates as well as best possible upper bound to the third Hankel determinant for the functions belong to this class.

References

1. [1]	Babalola, K.O. and Opoola, T.O. (2005), On coefficients of Certain analytic and univalent functions, Advances in Inequalities for Series, 1, 5-17.

2. [2]	Bazilevic, I.E. (1955), On a case of integrability in quadratures of the Loewner Kufarev equation, 37(79), 471-476.

3. [3]	Ehrenborg, R. (2000), The Hankel determinant of exponential polynomials, American Mathematical Monthly, 107, 557-560.

4. [4]	Gagandeep, S. and Gurcharanjit, S.(2015), On Third Hankel Determinant for a Subclass of Analytic Functions, Open Science Journal of Mathematics and Application, 3, 152-155.

5. [5]	Hayami, T. and Owa, S. (2009), Hankel determinant for $p$-valently starlike and convex functions of orser $\alpha$, General Math., 17, 29-44.

6. [6]	Juma, A.R.S., Abdulhussain, M.S., and Al-khafaji, S.N. (2018), Coefficient Bounds and Fekete-Szego inequalities for A class of Bazilevic type functions associated with new differential operator, Journal of Kufa for Mathematics and Computer, 5, 1-10.

7. [7]	Janteng, A., Halim, S.A., and Darus, M. (2007), Hankel determinant for starlike and convex functions, Int. J. Math. Anal., 13, 619-625.

8. [8]	Janteng, A., Halim, S.A., and Darus, M. (2006), Hankel determinant for functions starlike and convex with respect to symmetric points, Journal of Quality Measurement and Analysis, 2, 37-43.

9. [9]	Janteng, A., Halim, S.A., and Darus, M. (2006), Coefficient inequality for a function whose derivative has a positive real part, Journal of Inequalities in Pure and Applied Mathematics, 7, 1-5.

10. [10]	Krishna, D.V., Venkateswarlu, B., and Ramreddy, T. (2015), Third Hankel determinant for certain subclass of $p$-valent functions, Complex Variables and Elliptic Equations, 60, 1301-1307.

11. [11]	Keogh, F.R. and Merkes, E.P. (1969), A coe?cient inequality for certain classes of analytic functions, Proc. Amer. Math. Sco., 20, 8-12.

12. [12]	Libera, R.J. and Zlotkiewicz, E.J. (1982), Early coefficients of the invers of a regular convex function, Proceedings of the American Mathematical Society, 85, 225-230.

13. [13]	Miller, S.S. and Mocanu, P.T. (1981), Differential Subordination and univalent functions, Michigan. Math. J., 28, 157-171.

14. [14]	Noor, K.I. (1983), Hankel determinant problem for the class of functions with bounded boundary rotation, Revue Roumaine de Mathematiques Pures et Appliquees, 28, 731-739.

15. [15]	Patil, S.M. and Khairnar, S.M. (2017), Third Hankel Determinant for Starlike Function with respect to Symmetric Points, International Journal of Pure and Applied Mathematical Sciences, 10, 7-15.

16. [16]	Pommerenke, C.(1975), Univalent Functions, Vandenhoeck and Ruprecht, G\"{ottingen}.

17. [17]	Shanmugam, G., Stephen, B.A., and Babalola, K.O. (2014), Third Hankel Determinant for k-Starlike Functions, Gulf Journal of Mathematics 2, 107-113.