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Vol. 48 No. 4 (2022)
Serdica Mathematical Journal

Articles

Coefficient estimates for some generalized subclasses of analytic functions with respect to symmetric and conjugate points

https://doi.org/10.55630/serdica.2022.48.279-296

Published 07-12-2023

  • Gagandeep Singh
    • ,
  • Gurcharanjit Singh

Gagandeep Singh
Khalsa College

Gurcharanjit Singh
G.N.D.U. College

Abstract

In this paper, we introduce certain unified subclasses of close-to-convex functions and quasi-convex functions with respect to symmetric and conjugate points in the unit disc \(E=\left\{z\in\mathbb{C}:\mid z \mid<1\right\}\) and establish the upper bounds of the first four coefficients for these classes. This study will work as a motivation for the other researchers in this field to study some more similar classes.

2020 Mathematics Subject Classification:

30C45, 30C50

Keywords

univalent functions, close-to-convex functions, starlike functions with respect to symmetric points, subordination, conjugate points, coefficient bounds

Full text

Author Details

Gagandeep Singh

Department of Mathematics
Khalsa College
Amritsar-143001, Punjab, India
e-mail: kamboj.gagandeep@yahoo.in

Gurcharanjit Singh

G.N.D.U. College
Chungh(Tarn-Taran)-143304, Punjab, India
e-mail: dhillongs82@yahoo.com

References

  1. M. Acu, S. Owa. On some subclasses of univalent functions. J. Inequal. Pure Appl. Math., 6, 3 (2005), Article 70, 6 pp.
  2. T. Al-Hawary, B. A. Frasin, M. Darus. On certain subclass of analytic functions with fixed point, J. Appl. Math. (2013), Article Id. 312387, 8 pp.
  3. J. W. Alexander. Functions which map the interior of the unit circle upon simple regions, Ann. Math. (2), 17, 1 (1915), 12–22.
  4. R. M. El-Ashwah, D. K. Thomas. Some subclasses of close-to-convex functions, J. Ramanujan Math Soc. 2, 1 (1987), 85–100.
  5. R. N. Das, P. Singh. On subclasses of schlicht mappings, Indian J. Pure Appl. Math. 8, 8 (1977), 864–872.
  6. W. Janowski. Some extremal problems for certain families of analytic functions, I. Ann. Polon. Math. 28 (1973), 297–326.
  7. A. Janteng, S. A. Halim, M. Darus. Functions close-to-convex and quasi-convex with respect to other points, Int. J. Pure Appl. Math., 30, 2 (2006), 225–236.
  8. S. Kanas, F. Rønning. Uniformly starlike and convex functions and other related classes of univalent functions, Ann. Univ. Mariae Curie-Sklodowska, Section A, 53 (1999), 95–105.
  9. W. Kaplan. Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185.
  10. A. T. Oladipo. New subclasses of analytic functions with respect to other points. Int. J. Pure Appl. Math. 75, 1 (2012), 1–12.
  11. S. O. Olatunji, A. T. Oladipo. On a new subfamilies of analytic and Univalent functions with negative coefficient with respect to other points. Bull. Math. Anal. Appl. 3, 2 (2011), 159–166.
  12. K. Sakaguchi. On a certain univalent mapping. J. Math. Soc. Japan 11 (1959), 72–75.
  13. G. Singh, G. Singh. Certain subclasses of alpha-convex functions with fixed point. J. Appl. Math. Inform. 40, 1–2 (2022), 259–266.