The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order

Year 2023, Volume: 9 Issue: 1, 1 - 6, 30.06.2023

Nizami Mustafa , Veysel Nezir , Arzu Kankılıç

Abstract

In this paper, we give coefficient estimates for the certain subclass of analytic and univalent functions on the open unit disk in the complex plane associated with sine hyperbolic function with the complex order. For the defined here subclass , we obtain coefficient estimates for initial two coefficients and examine the Fekete-Szegö problem.

Keywords

Convex function, sine hyperbolic function, coefficient estimate, Fekete-Szegö problem, complex order

References

• ARMSTRONG, B., THÉRIAULT, G., GUÉNEL, P., DEADMAN, J., GOLDBERG, M., HÉROUX, P. (1994). Association between exposure to pulsed electromagnetic fields and cancer in electric utility workers in Quebec, Canada, and France. Am J Epidemiol 1994, 140:805-820.
• ALOTAİBİ, A., ARİF, M., ALGHAMDİ, M. A., HUSSAİN, S. (2020) Starlikness associated with cosine hyperbolic function. Mathematics. 8(7), p. 1118.
• ARİF, M., AHMAD, K., LİU, J.-L., SOKOL, J. (2019). A new class of analytic functions associated with Salagean operatör. Hindawi Journal of Function Spaces. Article ID 6157394, 8 pages https://doi.org/10.1155/2019/6157394
• BANO, K., RAZA, M. (2020) Starlike functions associated with cosine function. Bull. Iran. Math. Soc. 47: pp. 1513-1532.
• BİEBERBACH, L. (1916) Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln. Sitzungsberichte Preuss. Akad. Der Wiss. 138: pp. 940-955
• BRANNAN, D. A., KİRWAN, W. E. (1969) On some classes of bounded univalent functions. J. Lond. Math. Soc. 2: pp. 431-443.
• CHO, N. E., KUMAR, V., KUMAR, S. S., RAVİCHANDRAN, V. (2019) Radius problems for starlike functions associated with the sine function. Bull. Iran. Math. Soc. 45: pp. 213-232.
• DE BRANGES, L. (1985) A proof of the Bieberbach conjecture. Acta Math. 154: pp. 137-152.
• DUREN, P. L. (1983) Univalent Functions. In Grundlehren der Mathematischen Wissenschaften, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, Volume 259.
• JANOWSKİ, W. (1970) Extremal problems for a family of functions with positive real part and for some related families. Ann. Pol. Math. 23: pp. 159-177.
• KÖEBE, P. (1909) Über die Uniformisierrung der algebraishen Kurven, durch automorpher Funktionen mit imaginarer Substitutionsgruppe. Nachr. Akad. Wiss. Göttingen Math.-Phys. pp. 68-76.
• KUMAR, S. S., ARORA, K. (2020) Starlike functions associated with a petal shaped domain. ArŞiv: 2010.10072
• MA, W. C., MİNDA, D. (1994) A unified treatment of some special classes of univalent functions. In Proceedings of the Conference on Complex Analysis, Tianjin, China, Li, Z., Ren, F., Yang, L., Zhang, S., Eds.; Conference Proceedings and Lecture Notes in Analysis; Internotianal Press: Cambridge, MA, USA, Volume 1, pp. 157-169.
• MENDİRATTA, R., NAGPAL, S., RAVİCHANRAN, V. (2015) On a subclass of strongly starlike functions assiociated with exponential function. Bull. Malays. Math. Soc. 38, pp. 365-386.
• MİLLER, S. S. (1975) Differential inequalities and Caratheodory functions. Bull. Am. Math. Soc. 1975, 81, pp. 79-81.
• MUSTAFA N. KORKMAZ S. (2022) Coefficient Bound Estimates and Fekete-Szegö Problemfor a Certain Subclass of Analytic and Bi-univalent Functions. Turkish Journal of Science. 7(3), 211-218.
• MUSTAFA N. (2017) Fekete-Szegö Problem for certain subclass of analytic and bi-univalent functions. Journal of Scientific and Engineering Research. 4(8), 30–40.
• MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associted with sine hyperbolic function. 13th International Istanbul Scientific Research Congress on Life, Engineering and Applied Sciences on April 29-30: pp. 242-249, Istanbul, Turkey.
• SHARMA, K., JAİN, N. K., RAVİCHANRAN, V. (2016) Starlike function associated witha cardioid. Afr. Math. 27: pp. 923-939.
• SHİ,. L., SRİVASTAVA, H. M. ARİF, M., HUSSAİN, S., KHAN, H. (2019) An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function. Symmetry. 11: p.598. SOKOL, J. (2011). A certain class of starlike functions. Comput. Math. Appl. 62, pp. 611-619.
• SOKOL, J., STANKİEWCZ, J. (2021). Radius of conexity of some subclasses of strongy starlike functions. Zesyty Nauk. Bull. Sci. Math., 167, 102942.
• ULLAH, K., ZAİNAB, S., ARİF, M., DARUS, M., SHUTAYİ, M. (2021) Radius Problems for Starlike Functions Associated with the Tan Hyperbolic Function. Hindawi Journal of Function Spaces Volume 202, Article ID 9967640, 15 pages https://doi.org/10.1155/2021/9967640 .
• XU QH, XİAO G, SRİVASTAVA H.M. (2012) A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems. Applied Mathematics and Computation. 218, 11461–11465.