Some properties of Differential Subordination for the Subordination Class with the Generalized Derivative Operator

Eman Khleifa Shmella; Aisha Ahmed Amer

doi:10.58916/jhas.v9i2.270

المؤلفون

Eman Khleifa Shmella Mathematics Dept-Faculty of Science, Zliten - Alasmarya Islamic University, Libya مؤلف
Aisha Ahmed Amer Mathematics Dept-Faculty of Sciences, Khoms- El Mergib University, Libya مؤلف

DOI:

https://doi.org/10.58916/jhas.v9i2.270

الكلمات المفتاحية:

Convex functions, Cartesian multiplication, differential operator, stellar functions, dependency differential.

الملخص

In this paper ,we will using a generalized derivative operator in the unit disk which is defined by Hadamard product , and introduced differential Subordination for a new class define by this operator, and satisfy its specific relationship to derive the subordination for this operator by using properties of subordination concept .

التنزيلات

تنزيل البيانات ليس متاحًا بعد.

المراجع

Al-Oboudi, F. M. (2004). On univalent functions defined by a generalized Sălăgean operator. International Journal of Mathematics and Mathematical Sciences, 2004, 1429-1436.

Alabbar, N., Darus, M., & Amer, A. (2023). Coefficient Inequality and Coefficient Bounds for a New Subclass of Bazilevic Functions. Journal of Humanitarian and Applied Sciences, 8(16), 496-506.

Amer, A. A. (2016). Second Hankel Determinant for New Subclass Defined by a Linear Operator. Paper presented at the Computational Analysis: AMAT, Ankara, May 2015 Selected Contributions.

Amer, A. A., & Alabbar, N. M. (2017). Properties of Generalized Derivative Operator to A Certain Subclass of Analytic Functions with Negative Coefficients.

Amer, A. A., & Darus, M. (2011). On some properties for new generalized derivative operator. Jordan Journal of Mathematics and Statistics (JJMS), 4(2), 91-101.

Bieberbach, L. (1916). Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. Sitzungsberichte Preussische Akademie der Wissenschaften, 138, 940-955.

Cotîrlă, L.-I., & Juma, A. R. S. (2023). Properties of differential subordination and superordination for multivalent functions associated with the convolution operators. Axioms, 12(2), 169.

De Branges, L. (1985). A proof of the Bieberbach conjecture. Acta Mathematica, 154(1), 137-152.

Koebe, P. (1909). Ueber die Uniformisierung beliebiger analytischer Kurven.(Vierte Mitteilung). Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1909, 324-362.

Miller, S. S., & Mocanu, P. T. (2003). Subordinants of differential superordinations. Complex variables, 48(10), 815-826.

Ruscheweyh, S. (1975). New criteria for univalent functions. Proceedings of the American Mathematical Society, 49(1), 109-115.

Salagean, G. S. (2006). Subclasses of univalent functions. Paper presented at the Complex Analysis—Fifth Romanian-Finnish Seminar: Part 1 Proceedings of the Seminar held in Bucharest, June 28–July 3, 1981.

Shanmugam, T., Sivasubramanian, S., & Srivastava, H. (2006). Differential sandwich theorems for certain subclasses of analytic functions involving multiplier transformations. Integral Transforms and Special Functions, 17(12), 889-899.

Shaqsi, K., & Darus, M. (2008). An operator defined by convolution involving the polylogarithms functions. Journal of Mathematics and Statistics, 4(1), 46.

Shmella, E. K., & Amer, A. A. (2024). Estimation of the Bounds of Univalent Functional of Coefficients Apply the Subordination Method.