Applications on Geometric Function Theory using Symmetric Geometric Properties for a New Subclass of k-valent Functions
DOI:
https://doi.org/10.29304/jqcsm.2025.17.32404Keywords:
Analytic functions, open unit disk, extreme points, closure theoremAbstract
This study introduces a new class of k-valent analytic functions constructed through the Hadamard product within the open unit disk The paper explores several geometric characteristics of this class, including coefficient bounds, distortion and growth behavior, closure properties, radii related to convexity and starlikeness, as well as the determination of extreme points and weighted mean with some applications.
Downloads
References
S. A. Al-Ameedee, W. G. Atshan and F. A. Al-Maamori, Coefficients estimates of bi-univalent functions defined by new subclass function, Journal of Physics: Conference Series, 1530(1) (2020), 012105.
M. K. Aouf, “On a class of p-valent close-to-convex functions of order β and type α,” International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 294247, 8 pages, 1988.
M. K. Aouf, A. O. Mostafa, A. M. Shahin, and S. M. Madian, “Some inclusion relations for subclasses of p-valent functions defined by a multiplier transformation,” Acta Universitatis Apulensis, vol. 32, pp. 1–12, 2012.
W. G. Atshan and E. I. Badawi, Results on coefficient estimates for subclasses of analytic and bi-univalent functions, Journal of Physics: Conference Series, 1294 (2019), 032025.
W. G. Atshan, R. A. Hadi and S. Yalcin, Coefficient estimates for special subclasses of k-fold symmetric bi-univalent functions, Mathematics for Applications, 9(2) (2020), pp. 83-90.
T. Bulboacã, Differential Subordinations and Superordinations, Recent Results, House of Scientific book Publ, Cluj-Napoca, 2005.
M. El-Ityan, Q. A. Shakir, T. Al-Hawary, R. Buti, D. Breaz and L.-I. Cotîrlă, On the third Hankel determinant of a certain subclass of bi-univalent functions defined by (p,q)-derivative operator, Mathematics, 13 (2025), 1269.
B. Fiore, A. Ghoshal, and R. Ostrovsky, "Hadamard Product Arguments and Their Applications," IACR Cryptology ePrint Archive, 2024.
A. W. Goodman, “On the Schwarz-Christoffel transformation and p-valent functions,” Transactions of the American Mathematical Society, vol. 68, pp. 204–223, 1950.
D. Kumar and R. M. Ali, “Certain subclass of multivalent analytic functions associated with Hadamard product”, Mathematics, Vol, 7, no.1, pp. 1-14, 2019.
R. J. Libera, “Some radius of convexity problems,” Duke Mathematical Journal, vol. 31, pp. 143–158, 1964.
S. S. Miller and P. T. Mocanu, Subordinations of differential superordinations Complex Variables, Vol. 48, No. 10, pp. 815–825, 2003.
M. S. Muhammed and W. G. Atshan, Applications of Quasi-Subordination on Subclasses of bi-univalent Function Associated with Generalized Differential Operator, Journal of Al-Qadisiyah for Computer Science and Mathematics Vol.16(14) 2024.
M. S. Muhammed and W. G. Atshan, Coefficient Estimates and Fekete-Szegӧ Inequality for certain New Subclass of bi-Univalent Functions by Using Generalized Operator with Bernoulli Polynomials, Advances in Nonlinear Variational Inequalities,28(4s) (2025), pp.534-546.
S. Owa, “On certain classes of p-valent functions with negative coefficients,” Simon Stevin, vol. 59, pp. 385–402, 1985.
D. A. Pater and N. K. Thakare, “On convex hulls and extreme points of p-valent starlike and convex classes with applications,” Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie, vol. 27, no. 75, pp. 145–160, 1983.
Q. A. Shakir, A. S. Tayyah, D. Breaz, L.-I. Cotîrlă, E. Rapeanu and F. M. Sakar, Upper bounds of the third Hankel determinant for bi-univalent functions in crescent-shaped domains, Symmetry, 16 (2024), 1281.
Q. A. Shakir and W. G. Atshan, On third Hankel determinant for certain subclass of bi-univalent functions, Symmetry, 16 (2024), 239.
Q. A. Shakir and F. M. Sakar, On third-order differential subordination and superordination properties of analytic functions defined by Tayyah–Atshan fractional integral operator, Advances in Nonlinear Variational Inequalities, 28 (2025), Article 2528. https://doi.org/10.52783/anvi.v28.2528
Q. A. Shakir and W. G. Atshan, On sandwich results of univalent functions defined by generalized Abbas–Atshan operator, Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(4) (2023), 11–20.
Q. A. Shakir and W. G. Atshan, Third-order sandwich results for analytic univalent functions involving a new Hadamard product operator, Iraqi Journal of Science, (2025), 2868–2887.
Q. A. Shakir and W. G. Atshan, Some sandwich theorems for meromorphic univalent functions defined by a new Hadamard product operator, Nonlinear Functional Analysis and Applications, (2025), 331–344.
A. S. Tayyah and W. G. Atshan, New results on r,k,µ-Riemann-Liouville fractional operators in complex domain with applications, Fractal and Fractional, 8(3) (2024), 165.
B. Teodor, K. A. Mohamed, E. Nak, R. K. Stanislawa and O. Milutin, New trends in geometric function theory, International Jornal of Mathematical and Mathematical Science, Vol. 2010(2010), Article Id 906317, doi: 10.115/2010/906317.
A. N. Tikhonov and A. A. Samarskii, “Equations of mathematical Physics”, Dover Publications, 2011.
L. N. Trefethen, “Numerical Conformal Mapping”, Elsevier, 1986.
A. S. Tayyah, W. G. Atshan and G. I. Oros, Third-order differential subordination results for meromorphic functions associated with the inverse of the Legendre Chi function via the Mittag-Leffler identity, Mathematics, 13(13) (2025), 2089.
Z. S. Jafar and W. G. Atshan, New results on fourth-order differential subordination and superordination for meromorphic multivalent functions defined by a new differential operator, Aip Conference Proceedings, 3264(1)(2025), 050103.
B. K. Mihsin, W. G. Atshan, S. S. Alhily and A. A. Lupas, New Results on Fourth-Order Differential Subordination and Superordination for Univalent Analytic Functions Involving a Linear Operator, Symmetry, 14(2) (2022), 324.
A. K. Wanas, Q. A. Shakir and A. Catas, Coefficient estimates and symmetry analysis for certain families of bi-univalent functions defined by the q-Bernoulli polynomial, Symmetry, 17 (2025), 1532.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Waggas Galib Atshan, Saad Raheem Bakheet, Qasim Ali Shakir, Muhammed Salih Muhammed

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.








