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Best bound for λ- pseudo starlike functions

Year 2019, Volume: 68 Issue: 1, 538 - 545, 01.02.2019
https://doi.org/10.31801/cfsuasmas.434997

Abstract

In this paper, we obtain sharp upper bound to the second Hankel determinant for the functions belong to the class of λ- pseudo starlike functions, an interesting sub class of univalent functions defined in the open unit disc E={z:|z|<1}, using Toeplitz determinants.

References

  • Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals. Math., 17(1915), 12 -22.
  • Babalola, K. O., On λ-Pseudo- star like functions, J. Classical Anal., 3(2)(2013), 137-147.
  • de Branges de Bourcia, Louis, A proof of Bieberbach conjecture, Acta Math., 154(1-2)(1985), 137-152.
  • Duren, P. L., Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 1983.
  • Grenander U. and Szegö, G., Toeplitz forms and their applications. 2nd ed., New York (NY): Chelsea Publishing Co., 1984.
  • Janteng, A., Halim S. A. and Darus, M., Hankel Determinant for starlike and convex functions, Int. J. Math. Anal., 1(13)(2007), 619-625.
  • Libera R. J. and Zlotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in [mathscr]<LaTeX>\mathscr{P}</LaTeX>, Proc. Amer. Math. Soc., 87(2)(1983), 251-257.
  • Prajapat, J. K., Bansal, D., Singh Alok and Mishra, A. K., Bounds on third Hankel determinant for close-to-convex functions, Acta. Univ. Sapientiae, Mathematica, 7(2)(2015), 210-219.
  • Pommerenke, Ch., Univalent functions, Gottingen: Vandenhoeck and Ruprecht; 1975.
  • Pommerenke, Ch., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41(1) (1966), 111-122.
  • Simon, B., Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol.54, American mathematical society colloquium publications. Providence (RI): American Mathematical Society; 2005.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for multivalent bounded turning functions of order alpha, Probl. Anal. Issues Anal., 23(1)(2016), 45-54.
  • Vamshee Krishna D. and RamReddy, T., An upper bound to the second Hankel functional for the class of gamma- star like functions, Bull. Iran. Math. Soc., 41(6)(2015), 1327-1337.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for a function whose derivative has a positive real part of order alpha, Math. Bohem., 140(1)(2015), 43-52.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math., 44(6)(2014), 1941-1959.
Year 2019, Volume: 68 Issue: 1, 538 - 545, 01.02.2019
https://doi.org/10.31801/cfsuasmas.434997

Abstract

References

  • Alexander, J. W., Functions which map the interior of the unit circle upon simple regions, Annals. Math., 17(1915), 12 -22.
  • Babalola, K. O., On λ-Pseudo- star like functions, J. Classical Anal., 3(2)(2013), 137-147.
  • de Branges de Bourcia, Louis, A proof of Bieberbach conjecture, Acta Math., 154(1-2)(1985), 137-152.
  • Duren, P. L., Univalent functions, Vol. 259 of Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 1983.
  • Grenander U. and Szegö, G., Toeplitz forms and their applications. 2nd ed., New York (NY): Chelsea Publishing Co., 1984.
  • Janteng, A., Halim S. A. and Darus, M., Hankel Determinant for starlike and convex functions, Int. J. Math. Anal., 1(13)(2007), 619-625.
  • Libera R. J. and Zlotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in [mathscr]<LaTeX>\mathscr{P}</LaTeX>, Proc. Amer. Math. Soc., 87(2)(1983), 251-257.
  • Prajapat, J. K., Bansal, D., Singh Alok and Mishra, A. K., Bounds on third Hankel determinant for close-to-convex functions, Acta. Univ. Sapientiae, Mathematica, 7(2)(2015), 210-219.
  • Pommerenke, Ch., Univalent functions, Gottingen: Vandenhoeck and Ruprecht; 1975.
  • Pommerenke, Ch., On the coefficients and Hankel determinants of univalent functions, J. Lond. Math. Soc., s1-41(1) (1966), 111-122.
  • Simon, B., Orthogonal polynomials on the unit circle, part 1. Classical theory. Vol.54, American mathematical society colloquium publications. Providence (RI): American Mathematical Society; 2005.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for multivalent bounded turning functions of order alpha, Probl. Anal. Issues Anal., 23(1)(2016), 45-54.
  • Vamshee Krishna D. and RamReddy, T., An upper bound to the second Hankel functional for the class of gamma- star like functions, Bull. Iran. Math. Soc., 41(6)(2015), 1327-1337.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for a function whose derivative has a positive real part of order alpha, Math. Bohem., 140(1)(2015), 43-52.
  • Vamshee Krishna D. and RamReddy, T., Coefficient inequality for certain p-valent analytic functions, Rocky Mountain J. Math., 44(6)(2014), 1941-1959.
There are 15 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

D. Vamshee Krishna This is me 0000-0002-3334-9079

D. Shalini This is me 0000-0003-4059-8900

Publication Date February 1, 2019
Submission Date August 5, 2017
Acceptance Date February 1, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA Krishna, D. V., & Shalini, D. (2019). Best bound for λ- pseudo starlike functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 538-545. https://doi.org/10.31801/cfsuasmas.434997
AMA Krishna DV, Shalini D. Best bound for λ- pseudo starlike functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):538-545. doi:10.31801/cfsuasmas.434997
Chicago Krishna, D. Vamshee, and D. Shalini. “Best Bound for λ- Pseudo Starlike Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 538-45. https://doi.org/10.31801/cfsuasmas.434997.
EndNote Krishna DV, Shalini D (February 1, 2019) Best bound for λ- pseudo starlike functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 538–545.
IEEE D. V. Krishna and D. Shalini, “Best bound for λ- pseudo starlike functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 538–545, 2019, doi: 10.31801/cfsuasmas.434997.
ISNAD Krishna, D. Vamshee - Shalini, D. “Best Bound for λ- Pseudo Starlike Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 538-545. https://doi.org/10.31801/cfsuasmas.434997.
JAMA Krishna DV, Shalini D. Best bound for λ- pseudo starlike functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:538–545.
MLA Krishna, D. Vamshee and D. Shalini. “Best Bound for λ- Pseudo Starlike Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 538-45, doi:10.31801/cfsuasmas.434997.
Vancouver Krishna DV, Shalini D. Best bound for λ- pseudo starlike functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):538-45.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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