A certain subclass of starlike functions defined by subordination

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In the present paper, we introduce and investigate a new result connected to subclasses of normalized and univalent functions in the open unit disk. Some majorization results and geometric properties such as radii of starlikeness, convexity, pre-Schwarzian norm and coefficient estimates are obtained.

Keywords

Main Subjects


[1] Lee, S. K., Ali, R. M., Ravichandran, V., & Supramaniam, S. (2011). The Fekete-Szego coecient functional for transforms of analytic functions. Bulletin of the Iranian mathematical society, 35(2), 119-142.
[2] Ali, R. M., Ravichandran, V., & Seenivasagan, N. (2007). Coecient bounds for p-valent functions. Applied Mathematics and Computation, 187(1), 35-46. https://doi.org/10.1016/j.amc.2006.08.100
[3] Bano, K., & Raza, M. (2021). Starlike functions associated with cosine functions. Bulletin of the Iranian Mathematical Society, 47, 1513-1532. https://doi.org/10.1007/s41980-020-00456-9
[4] Becker, J., & Pommerenke, C. (1984). Schlichtheitskriterien und Jordangebiete. 
[5] Caratheodory, C. (2021). Theory of Functions of a Complex Variable, Vol 1 (Vol. 97). American Mathematical Soc.
[6] Cho, N. E., Kumar, V., Kumar, S. S., & Ravichandran, V. (2019). Radius problems for starlike functions associated with the sine function. Bulletin of the Iranian Mathematical Society, 45, 213-232. https://doi.org/10.1007/s41980-018-0127-5
[7] Duren, P. L. (2001). Univalent functions (Vol. 259). Springer Science & Business Media. 
[8] Janowski, W. (1970). Extremal problems for a family of functions with positive real part and for some related families. In Annales Polonici Mathematici (Vol. 23, pp. 159-177). Instytut Matematyczny Polskiej Akademii Nauk. 
[9] Kanas, S., Masih, V. S., & Ebadian, A. (2019). Relations of a planar domains bounded by hyperbolas with families of holomorphic functions. Journal of Inequalities and Applications, 2019, 1-14. https://doi.org/10.1186/s13660-019-2190-8
[10] Kargar, R., Ebadian, A., & Soko l, J. (2019). On Booth lemniscate and starlike functions. Analysis and Mathematical Physics, 9, 143-154. https://doi.org/10.1007/s13324-017-0187-3
[11] Kargar, R., & Trojnar-Spelina, L. (2021). Starlike functions associated with the generalized Koebe function. Analysis and Mathematical Physics, 11, 1-26. https://doi.org/10.1007/s13324-021-00579-0
[12] Kargar, R., SOKOL, J., Ebadian, A., & Trojnar-Spelina, L. (2018, January). On a class of starlike functions related with Booth lemniscate. In Proceedings of the Jangjeon Mathematical Society (Vol. 21, No. 3, pp. 479-486). https://doi.org/10.17777/pjms2018.21.3.479
[13] Kumar, S. S., & Arora, K. (2020). Starlike functions associated with a petal shaped domain. arXiv preprint arXiv:2010.10072. 
[14] Kumar, V., Cho, N. E., Ravichandran, V., & Srivastava, H. M. (2019). Sharp coecient bounds for starlike functions associated with the Bell numbers. Mathematica Slovaca, 69(5), 1053-1064. https://doi.org/10.1515/ms-2017-0289
[15] Kumar, S., & Ravichandran, V. (2016). A Subclass of Starlike Functions Associated With a Rational Function. Southeast Asian Bulletin of Mathematics, 40(2). 
[16] MacGregor, T. H. (1967). Majorization by univalent functions. Duke Mathematical Journal, 34, 95{102. 
[17] Ma, W. (1992). A uni ed treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis, 1992. International Press Inc. 
[18] Mendiratta, R., Nagpal, S., & Ravichandran, V. (2015). On a subclass of strongly starlike functions associated with exponential function. Bulletin of the Malaysian Mathematical Sciences Society, 38, 365-386. https://doi.org/10.1007/s40840-014-0026-8
[19] Nehari, Z. (1952). Conformal Mapping, McGrow-Hill Book Co. Inc., New york. 
[20] Robertson, M. S. (1985). Certain classes of starlike functions. Michigan Mathematical Journal, 32(2), 135-140.
[21] Rahrovi, S., Piri, H., & Kargar, R. (2021). The behavior of starlike functions exterior of parabola. Houston Journal of Mathematics, 47(4), 723-743. 
[22] Raina, R. K., & Soko l, J. (2015). Some properties related to a certain class of starlike functions. Comptes Rendus Mathematique, 353(11), 973-978. https://doi.org/10.1016/j.crma.2015.09.011
[23] Sharma, K., Jain, N. K., & Ravichandran, V. (2016). Starlike functions associated with a cardioid. Afrika Matematika, 27, 923-939. https://doi.org/10.1007/s13370-015-0387-7
[24] Soko l, J. (2011). A certain class of starlike functions. Computers & Mathematics with Applications, 62(2), 611-619. https://doi.org/10.1016/j.camwa.2011.05.041
[25] Soko l, J., & Stankiewicz, J. (1996). Radius of convexity of some subclasses of strongly starlike functions. Zeszyty Nauk. Politech. Rzeszowskiej Mat, 19, 101-105. 
[26] Uralegaddi, B. A., Ganigi, M. D., & Sarangi, S. M. (1994). Univalent functions with positive coecients. Tamkang Journal of Mathematics, 25(3), 225-230. https://doi.org/10.5556/j.tkjm.25.1994.4448