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Year 2024, Volume: 10 Issue: 2, 37 - 46, 31.12.2024

Arzu Kankılıç , Nizami Mustafa , Veysel Nezir

Abstract

References

  • ALOTAIBI, A., ARIF, M., ALGHAMDI, M. A., HUSSAIN, S. (2020) Starlikness associated with cosine hyperbolic function. Mathematics. 8(7), p. 1118.
  • ARIF, M., AHMAD, K., LIU, J.-L., SOKOL, J. (2019) A new class of analytic functions associated with Salagean operator. 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.
  • BRANNAN, D. A., KIRWAN, W. E. (1969) On some classes of bounded univalent functions. J. Lond. Math. Soc. 2, pp. 431-443.
  • BIEBERBACH, L. (1916) Über die Koeffizienten derjenigen Potenzreihen welche eine schlichte Abbidung des Einbeiskreises vermitteln. Sitzungsberichte Preuss. Akad. Der Wiss. 138, pp. 940- 955.
  • CARATHEODORY, C. (1907) Über den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene werte nicht annehmen. Math. Ann. 64, pp.95-115.
  • CHO, N. E., KUMAR, V., KUMAR, S. S., RAVICHANDRAN, 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.
  • FRASIN, B. AND AOUF, M.K. (2011) New Subclasses of Bi-univalent Functions. Applied Mathematics Letters. 24(9), pp. 1569-1573.
  • JANOWSKI, 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.
  • SOKOL, J. A certain class of starlike functions. Comput. Math. Appl. 2011, 62, pp. 611-619.
  • KANKILIÇ. A., MUSTAFA, N. (2024a) On the Pseudo Starlike Bi-univalent Function Class of Complex Order. Journal of Scientific and Engineering Research. 11(5), pp. 26-34.
  • KANKILIÇ. A., MUSTAFA, N. (2024b) On the Pseudo Convex Bi-univalent Function Class of Complex Order. Journal of Scientific and Engineering Research. 11(7). pp. 259-267.
  • KÖEBE, P. (1909) Über die Uniformisierrung der algebraishen Kurven, durch automorpher Funktionen mit imaginarer Substitutions gruppe. Nachr. Akad. Wiss. Göttingen Math. -Phys. pp. 68-76.
  • KUMAR, S. S., ARORA, K. (2020) Starlike functions associated with a petal shaped domain. arXiv: 2010.10072.
  • MENDIRATTA, R., NAGPAL, S., RAVICHANDRAN, V. (2015) On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Soc. 38, pp. 365-386.
  • MILLER, S. S. (1975) Differential inequalities and Caratheodory functions. Bull. Am. Math. Soc. 81, pp. 79-81.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023a) Coefficient estimates for certain subclass of analytic and univalent functions associated 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., NEZIR, V., KANKILIÇ. A. (2023b) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated 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.
  • MUSTAFA, N., NEZIR, V. (2023) Coefficient estimates and Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function. 13th International Istanbul Scientific Research Congress on Life, Engineering and Applied Sciences on May 1-2, pp. 475-481, Istanbul, Türkiye.
  • MUSTAFA, N., DEMIR, H. A. (2023a) 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. 2555- 2563, Rize Turkey.
  • MUSTAFA, N., DEMIR, H. A. (2023b) Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June 6-8, pp. 2564-2572, Rize Turkey.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023c) Coefficient estimates for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Journal of Scientific and Engineering Research. 10(6), pp.18-25.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023d) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Eastern Anatolian Journal of Science. 9(1), pp. 1-6.
  • MUSTAFA, N., DEMIR, 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.
  • SHARMA, K., JAIN, N. K., RAVICHANDRAN, V. (2016) Starlike function associated with a cardioid. Afr. Math. 27, pp. 923-939.
  • SHI, L., SRIVASTAVA, H. M. ARIF, M., HUSSAIN, 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., STANKIEWCZ, J. (1996) Radius of convexity of some subclasses of strongly starlike functions. Zesz. Nauk. Politech. Rzesz. Math. vol.19, pp.101–105.
  • ULLAH, K., ZAINAB, S., ARIF, M., DARUS, M., SHUTAYI, M. (2021) Radius Problems for Starlike Functions Associated with the Tan Hyperbolic Function. Hindawi Journal of Function Spaces.2021, 9967640.

On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order

Year 2024, Volume: 10 Issue: 2, 37 - 46, 31.12.2024

Arzu Kankılıç , Nizami Mustafa , Veysel Nezir

Abstract

In this paper, we defined a new subclass of starlike and convex bi-univalent functions and examine some geometric properties this function class. For this defination class, we gave some coefficient estimates and solve Fekete-Sezöge problem.

Keywords

Starlike function convex function pseudo starlike function pseudo convex function

References

  • ALOTAIBI, A., ARIF, M., ALGHAMDI, M. A., HUSSAIN, S. (2020) Starlikness associated with cosine hyperbolic function. Mathematics. 8(7), p. 1118.
  • ARIF, M., AHMAD, K., LIU, J.-L., SOKOL, J. (2019) A new class of analytic functions associated with Salagean operator. 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.
  • BRANNAN, D. A., KIRWAN, W. E. (1969) On some classes of bounded univalent functions. J. Lond. Math. Soc. 2, pp. 431-443.
  • BIEBERBACH, L. (1916) Über die Koeffizienten derjenigen Potenzreihen welche eine schlichte Abbidung des Einbeiskreises vermitteln. Sitzungsberichte Preuss. Akad. Der Wiss. 138, pp. 940- 955.
  • CARATHEODORY, C. (1907) Über den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene werte nicht annehmen. Math. Ann. 64, pp.95-115.
  • CHO, N. E., KUMAR, V., KUMAR, S. S., RAVICHANDRAN, 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.
  • FRASIN, B. AND AOUF, M.K. (2011) New Subclasses of Bi-univalent Functions. Applied Mathematics Letters. 24(9), pp. 1569-1573.
  • JANOWSKI, 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.
  • SOKOL, J. A certain class of starlike functions. Comput. Math. Appl. 2011, 62, pp. 611-619.
  • KANKILIÇ. A., MUSTAFA, N. (2024a) On the Pseudo Starlike Bi-univalent Function Class of Complex Order. Journal of Scientific and Engineering Research. 11(5), pp. 26-34.
  • KANKILIÇ. A., MUSTAFA, N. (2024b) On the Pseudo Convex Bi-univalent Function Class of Complex Order. Journal of Scientific and Engineering Research. 11(7). pp. 259-267.
  • KÖEBE, P. (1909) Über die Uniformisierrung der algebraishen Kurven, durch automorpher Funktionen mit imaginarer Substitutions gruppe. Nachr. Akad. Wiss. Göttingen Math. -Phys. pp. 68-76.
  • KUMAR, S. S., ARORA, K. (2020) Starlike functions associated with a petal shaped domain. arXiv: 2010.10072.
  • MENDIRATTA, R., NAGPAL, S., RAVICHANDRAN, V. (2015) On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Soc. 38, pp. 365-386.
  • MILLER, S. S. (1975) Differential inequalities and Caratheodory functions. Bull. Am. Math. Soc. 81, pp. 79-81.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023a) Coefficient estimates for certain subclass of analytic and univalent functions associated 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., NEZIR, V., KANKILIÇ. A. (2023b) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated 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.
  • MUSTAFA, N., NEZIR, V. (2023) Coefficient estimates and Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function. 13th International Istanbul Scientific Research Congress on Life, Engineering and Applied Sciences on May 1-2, pp. 475-481, Istanbul, Türkiye.
  • MUSTAFA, N., DEMIR, H. A. (2023a) 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. 2555- 2563, Rize Turkey.
  • MUSTAFA, N., DEMIR, H. A. (2023b) Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine and cosine functions. 4th International Black Sea Congress on Modern Scientific Research on June 6-8, pp. 2564-2572, Rize Turkey.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023c) Coefficient estimates for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Journal of Scientific and Engineering Research. 10(6), pp.18-25.
  • MUSTAFA, N., NEZIR, V., KANKILIÇ. A. (2023d) The Fekete-Szegö problem for certain subclass of analytic and univalent functions associated with sine hyperbolic function with complex order. Eastern Anatolian Journal of Science. 9(1), pp. 1-6.
  • MUSTAFA, N., DEMIR, 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.
  • SHARMA, K., JAIN, N. K., RAVICHANDRAN, V. (2016) Starlike function associated with a cardioid. Afr. Math. 27, pp. 923-939.
  • SHI, L., SRIVASTAVA, H. M. ARIF, M., HUSSAIN, 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., STANKIEWCZ, J. (1996) Radius of convexity of some subclasses of strongly starlike functions. Zesz. Nauk. Politech. Rzesz. Math. vol.19, pp.101–105.
  • ULLAH, K., ZAINAB, S., ARIF, M., DARUS, M., SHUTAYI, M. (2021) Radius Problems for Starlike Functions Associated with the Tan Hyperbolic Function. Hindawi Journal of Function Spaces.2021, 9967640.
There are 29 citations in total.

Details

Primary Language English
Subjects Numerical and Computational Mathematics (Other)
Journal Section makaleler
Authors

Arzu Kankılıç 0009-0009-4543-9918

Nizami Mustafa 0000-0002-2758-0274

Veysel Nezir 0000-0001-9640-8526

Early Pub Date December 28, 2024
Publication Date December 31, 2024
Submission Date July 19, 2024
Acceptance Date December 18, 2024
Published in Issue Year 2024 Volume: 10 Issue: 2

Cite

APA Kankılıç, A., Mustafa, N., & Nezir, V. (2024). On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order. Eastern Anatolian Journal of Science, 10(2), 37-46.
AMA Kankılıç A, Mustafa N, Nezir V. On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order. Eastern Anatolian Journal of Science. December 2024;10(2):37-46.
Chicago Kankılıç, Arzu, Nizami Mustafa, and Veysel Nezir. “On the Pseudo Starlike and Pseudo Convex Bi-Univalent Function Classes of Complex Order”. Eastern Anatolian Journal of Science 10, no. 2 (December 2024): 37-46.
EndNote Kankılıç A, Mustafa N, Nezir V (December 1, 2024) On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order. Eastern Anatolian Journal of Science 10 2 37–46.
IEEE A. Kankılıç, N. Mustafa, and V. Nezir, “On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order”, Eastern Anatolian Journal of Science, vol. 10, no. 2, pp. 37–46, 2024.
ISNAD Kankılıç, Arzu et al. “On the Pseudo Starlike and Pseudo Convex Bi-Univalent Function Classes of Complex Order”. Eastern Anatolian Journal of Science 10/2 (December 2024), 37-46.
JAMA Kankılıç A, Mustafa N, Nezir V. On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order. Eastern Anatolian Journal of Science. 2024;10:37–46.
MLA Kankılıç, Arzu et al. “On the Pseudo Starlike and Pseudo Convex Bi-Univalent Function Classes of Complex Order”. Eastern Anatolian Journal of Science, vol. 10, no. 2, 2024, pp. 37-46.
Vancouver Kankılıç A, Mustafa N, Nezir V. On the Pseudo Starlike and Pseudo Convex Bi-univalent Function Classes of Complex Order. Eastern Anatolian Journal of Science. 2024;10(2):37-46.