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Year 2023, Volume: 9 Issue: 2, 10 - 15, 31.12.2023

Nizami Mustafa Hacı Ahmet Demir

Abstract

References

  • 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., DEMİR, H. A. (2023) Coefficient estimates for certain subclass of analytic and univalent functions with associated with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June 6-8, pp. 2264-2272, Rize Turkey.
  • MUSTAFA, N., DEMİR, H. A. (2023) Fekete-Szegö problem for certain subclass of analytic and univalent functions associted with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June pp. 2255-2263, Rize Turkey.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023). Coefficient estimates for certain subclass of analytic and univalent functions associted with sine hyperbolic function with complex order. Journal of Scientific and Engineering Research, 10(6): pp.18-25.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associted with sine hyperbolic function with complex order. Eastern Anatolian Journal of Science, 9(1), pp. 1-6.
  • MUSTAFA, N., DEMİR, H. A. (2023) Coefficient estimates for certain subclass of analytic and univalent functions with associated with sine and cosine functions with complex order. Journal of Scientific and Engineering Research, 10(6): pp. 131-140.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023) Coefficient estimates 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. 234-241, Istanbul, Turkey
  • 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 .

Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order

Year 2023, Volume: 9 Issue: 2, 10 - 15, 31.12.2023

Nizami Mustafa Hacı Ahmet Demir

Abstract

The main focus of this paper is to give some coefficient estimates for the analytic and univalent functions on the open unit disk in the complex plane that are subordinated to cosine and sine functions of complex order. For the defined here subclass of analytic and univalent functions , with the quantity

subordinated to , we obtain the coefficient estimates for the initial two coefficients and examine the Fekete-Szegö problem.

Keywords

Starlike function convex function cosine function sine function coefficient estimate Fekete-Szegö problem complex order

References

  • 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., DEMİR, H. A. (2023) Coefficient estimates for certain subclass of analytic and univalent functions with associated with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June 6-8, pp. 2264-2272, Rize Turkey.
  • MUSTAFA, N., DEMİR, H. A. (2023) Fekete-Szegö problem for certain subclass of analytic and univalent functions associted with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June pp. 2255-2263, Rize Turkey.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023). Coefficient estimates for certain subclass of analytic and univalent functions associted with sine hyperbolic function with complex order. Journal of Scientific and Engineering Research, 10(6): pp.18-25.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associted with sine hyperbolic function with complex order. Eastern Anatolian Journal of Science, 9(1), pp. 1-6.
  • MUSTAFA, N., DEMİR, H. A. (2023) Coefficient estimates for certain subclass of analytic and univalent functions with associated with sine and cosine functions with complex order. Journal of Scientific and Engineering Research, 10(6): pp. 131-140.
  • MUSTAFA, N., NEZİR, V., KANKILIÇ. A. (2023) Coefficient estimates 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. 234-241, Istanbul, Turkey
  • 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 .
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Methods and Special Functions
Journal Section makaleler
Authors

Nizami Mustafa 0000-0002-2758-0274

Hacı Ahmet Demir This is me 0009-0004-5158-6467

Publication Date December 31, 2023
Published in Issue Year 2023 Volume: 9 Issue: 2

Cite

APA Mustafa, N., & Demir, H. A. (2023). Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order. Eastern Anatolian Journal of Science, 9(2), 10-15.
AMA Mustafa N, Demir HA. Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order. Eastern Anatolian Journal of Science. December 2023;9(2):10-15.
Chicago Mustafa, Nizami, and Hacı Ahmet Demir. “Fekete-Sezegö Problem for Certain Subclass of Analytic and Univalent Functions Associated With Cosine and Sine Functions of Complex Order”. Eastern Anatolian Journal of Science 9, no. 2 (December 2023): 10-15.
EndNote Mustafa N, Demir HA (December 1, 2023) Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order. Eastern Anatolian Journal of Science 9 2 10–15.
IEEE N. Mustafa and H. A. Demir, “Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order”, Eastern Anatolian Journal of Science, vol. 9, no. 2, pp. 10–15, 2023.
ISNAD Mustafa, Nizami - Demir, Hacı Ahmet. “Fekete-Sezegö Problem for Certain Subclass of Analytic and Univalent Functions Associated With Cosine and Sine Functions of Complex Order”. Eastern Anatolian Journal of Science 9/2 (December 2023), 10-15.
JAMA Mustafa N, Demir HA. Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order. Eastern Anatolian Journal of Science. 2023;9:10–15.
MLA Mustafa, Nizami and Hacı Ahmet Demir. “Fekete-Sezegö Problem for Certain Subclass of Analytic and Univalent Functions Associated With Cosine and Sine Functions of Complex Order”. Eastern Anatolian Journal of Science, vol. 9, no. 2, 2023, pp. 10-15.
Vancouver Mustafa N, Demir HA. Fekete-Sezegö problem for certain subclass of analytic and univalent functions associated with cosine and sine functions of complex order. Eastern Anatolian Journal of Science. 2023;9(2):10-5.