Coefficient Estimates for Certain Subclasses of Analytic Functions Defined by New Differential Operator

Öz

The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory in Complex Analysis and its related fields. Many derivative and integral operators can be written in terms of convolution of certain analytic functions. The class of analytic functions, which has an essential place in the theory of geometric functions, has been studied by many researchers before. This topic still maintains its popularity today. In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order r.

Anahtar Kelimeler

• Analytic functions
• coefficient bounds
• differential operator
• subordination

Kaynakça

1. 1. Al-Hawary, T., Frasin, B. A., Yousef, F. 2018. Coefficients estimates for certain classes of analytic functions, Afrika Mathematika, 29, 1265-1271.
2. 2. Al-Oboudi, F. M. 2004. On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci. 27, 1429-1436.
3. 3. Cho, N. M., Kim, T. H. 2003. Multiplier transformations and strongly close to convex functions, Bull. Korean Math. Soc. 40-3, 399-410.
4. 4. Cho, N. M., Srivastava, H. M. 2003. Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling 37-1-2, 39-49.
5. 5. Miller, S. S., Mocanu, P. T., Differential subordination, Monographs and Textbooks in Pure and Applied Mathematics,. Marcel Dekker Inc. New York, 2000; pp 225.
6. 6. Robertson, M. S. 1936. On the theory of univalent functions, Annals of Mathematics 37, 374-408.
7. 7. Rogosinski, W. 1943. On the coefficients of subordinate functions, Proc. Lond. Math. Soc. (Ser 2) 48, 48-82.
8. 8. Salagean, G. 1983. Subclasses of univalent functions, Lecture Notes in Math., Springer Verlag, Berlin 1013, 362-372.

9. 9. Silverman, H. 1978. Subclasses of starlike functions, Rev. Roum. Math. Pures et Appl. 23, 1093-1099.
10. 10. Swamy, S. R. 2012. Inclusion properties of certain subclasses of analytic functions, Int. Math. Forum 7-36, 1751-1760.
11. 11. Wanas, A. K. 2019. New differential operator for holomorphic functions, Earthline Journal of Mathematical Sciences 2-2, 527-537. 12. Galib Atshan, W., Ibrahim Badawi, E., 2019. On Sandwich Theorems for Certain Univalent Functions Defined by a New operator. Journal of Al-Qadisiyah for Computer Science and Mathematics, 11(2), math 72-80.
12. 13. Atshan, W. G., Abbas, I. A., Yalcin, S., 2020. New Concept on Fourth-Order Differential Subordination and Superordination with Some Results for Multivalent Analytic Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Math Page 96-107.
13. 14. Frasin, B., & Murugusundaramoorthy, G., 2020. A subordination results for a class of analytic functions defined by q-differential operator, Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (published online ahead of print 2020).
14. 15. Çakmak, S., Yalçın, S., & Altınkaya, Ş., 2019. An application of the power series distribution for certain analytic univalent function classes. Lıbertas Mathematıca (new series), 39(1), 95-102. 16. Srivastava, H. M., & El-Deeb, S. M., 2020. A certain class of analytic functions of complex order connected with a q-analogue of integral operators. Miskolc Mathematical Notes, 21(1), 417-433.
15. 17. Khan, B., Srivastava, H. M., Khan, N., Darus, M., Tahir, M., & Ahmad, Q. Z., 2020. Coefficient estimates for a subclass of analytic functions associated with a certain leaf-like domain. Mathematics, 8(8), 1334.
16. 18. Liu, G., Liu, Z., & Ponnusamy, S., 2020. Refined Bohr inequality for bounded analytic functions. arXiv preprint arXiv:2006.08930.
17. 19. Porwal, S. 2020. Mapping Properties Of Certain Subclasses Of Analytic Functions Associated With Generalized Distribution Series. Applied Mathematics E-Notes, 20, 39-45.
18. 20. Atshan, W. G., Abbas, I. A., & Yalcin, S., 2020. New Concept on Fourth-Order Differential Subordination and Superordination with Some Results for Multivalent Analytic Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(1), Math Page 96-107.