Bounds on Toeplitz Determinant for Starlike Functions with Respect to Conjugate Points

Article Sidebar

PDF
Cite as:
Daud Mohamad, Nur Hazwani Aqilah Abdul Wahid, Bounds on Toeplitz Determinant for Starlike Functions with Respect to Conjugate Points, Int. J. Anal. Appl., 19 (3) (2021), 477-493.

Main Article Content

Daud Mohamad, Nur Hazwani Aqilah Abdul Wahid

Abstract

This paper is concerned with the estimate of the upper bounds of the Toeplitz determinants |T2(3)| and |T3(3)| for functions belonging to the subclass of starlike functions with respect to conjugate points. The results presented would extend the results for some existing subclasses in the literature.

Article Details

References

  1. I. Graham, Geometric function theory in one and higher dimensions, CRC Press, New York, 2003.
  2. S. S. Miller, P. T. Mocanu, Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65(2) (1978), 289-305.
  3. S. S. Miller, P. T. Mocanu, Differential subordinations and univalent functions, Michigan Math. J. 28(2) (1981), 157-172.
  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. S. Halim, Functions starlike with respect to other points, Int. J. Math. Math. Sci. 14(3) (1991), 451-456.
  6. S. A. F. M. Dahhar, A. Janteng, A subclass of starlike functions with respect to conjugate points, Int. Math. Forum, 4(28) (2009), 1373-1377.
  7. N. H. A. A. Wahid, D. Mohamad, S. Cik Soh, On a subclass of tilted starlike functions with respect to conjugate points, Menemui Mat. (Discover. Math.) 37(1) (2015), 1-6.
  8. K. Ye, L. H. Lim, Every matrix is a product of Toeplitz matrices, Found. Comput. Math. 16(3) (2016), 577-598.
  9. D. K. Thomas and S. A. Halim, Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions, Bull. Malaysian Math. Sci. Soc. 40(4) (2016), 1781-1790.
  10. V. Radhika, S. Sivasubramanian, G. Murugusundaramoorthy, J. M. Jahangiri, Toeplitz matrices whose elements are the coefficients of functions with bounded boundary rotation, J. Complex Anal. 2016 (2016), Art. ID 4960704.
  11. S. Sivasubramanian, M. Govindaraj, G. Murugusundaramoorthy, Toeplitz matrices whose elements are the coefficients of analytic functions belonging to certain conic domains, Int. J. Pure Appl. Math. 109(10) (2016), 39-49.
  12. C. Ramachandran, D. Kavitha, Toeplitz determinant for some subclasses of analytic functions, Glob. J. Pure Appl. Math. 13(2) (2017), 785-793.
  13. N. Magesh, Ş. Altinkaya, S. Yalçın, Construction of Toeplitz matrices whose elements are the coefficients of univalent functions associated with q-derivative operator, ArXiv:1708.03600 [Math]. (2017).
  14. M. F. Ali, D. K. Thomas, A. Vasudevarao, Toeplitz determinants whose elements are the coefficients of analytic and univalent functions, Bull. Aust. Math. Soc. 97(2) (2018), 253-264.
  15. V. Radhika, J. M. Jahangiri, S. Sivasubramanian, G. Murugusundaramoorthy, Toeplitz matrices whose elements are coefficients of BazileviÄ functions, Open Math. 16(1) (2018), 1161-1169.
  16. H. M. Srivastava, Q. Z. Ahmad, N. Khan, B. Khan, Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain, Mathematics, 7(2) (2019), 181.
  17. H. Y. Zhang, R. Srivastava, H. Tang, Third-order Hankel and Toeplitz determinants for starlike functions connected with the sine function, Mathematics, 7(5) (2019), 404.
  18. S. N. Al-Khafaji, A. Al-Fayadh, A. H. Hussain, S. A. Abbas, Toeplitz Determinant whose Its Entries are the Coefficients for Class of Non-Bazilevic Functions, J. Phys.: Conf. Ser. 1660 (2020), 012091.
  19. P. L. Duren, Univalent Functions vol. 259, Springer, New York-Berlin-Heidelberg-Tokyo, 1983.
  20. I. Efraimidis, A generalization of Livingston's coefficient inequalities for functions with positive real part, J. Math. Anal. Appl. 435(1) (2016), 369-379.