Nasze serwisy używają informacji zapisanych w plikach cookies. Korzystając z serwisu wyrażasz zgodę na używanie plików cookies zgodnie z aktualnymi ustawieniami przeglądarki, które możesz zmienić w dowolnej chwili. Więcej informacji odnośnie plików cookies.

Obowiązek informacyjny wynikający z Ustawy z dnia 16 listopada 2012 r. o zmianie ustawy – Prawo telekomunikacyjne oraz niektórych innych ustaw.

Wyłącz komunikat

 
 

Logowanie

Logowanie za pomocą Centralnej Usługi Uwierzytelniania PRz. Po zakończeniu pracy nie zapomnij zamknąć przeglądarki.

Journal of Mathematics and Applications

Journal of Mathematics and Applications
14/41, DOI: 10.7862/rf.2018.14

An Upper Bound for Third Hankel Determinant of Starlike Functions Related to Shell-like Curves Connected with Fibonacci Numbers

Janusz Sokół, Sedat İlhan, H. Özlem Güney

DOI: 10.7862/rf.2018.14

Abstract

We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.

Full text (pdf)

References

  1. K.O. Babalola, On H_3(1) Hankel determinant for some classes of univalent functions, Ineq. Theory Appl. 6 (2007) 1-7.
  2. D. Bansal, S. Maharana, J.K. Prajapat, Third order Hankel determinant for certain univalent functions, J. Korean Math. Soc. 52 (6) (2015) 1139-1148.
  3. R. Ehrenborg, The Hankel determinant of exponential polynomials, Amer. Math. Monthly 107 (2000) 557-560.
  4. M. Fekete, G. Szegö, Eine Bemerkung über ungerade schlichte Funktionen, J. London Math. Soc. 8 (1933) 85-89.
  5. A. Janteng, S. Halim, M. Darus, Coefficient inequality for a function whose derivative has a positive real part, J. Inequal. Pure Appl. Math. 7 (2) (2006) Article 50.
  6. A. Janteng, S. Halim, M. Darus, Hankel determinant for starlike and convex functions, Int. J. Math. Anal. 1 (13) (2007) 619-625.
  7. F.R. Keogh, E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969) 8-12.
  8. J.W. Layman, The Hankel transform and some of its properties, J. Integer Sequences 4 (2001) 1-11.
  9. R.J. Libera, E.J. Złotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2) (1983) 251-257.
  10. J.W. Noonan, D.K. Thomas, On the second Hankel determinant of areally mean p-valent functions, Trans. Amer. Math. Soc. 223 (2) (1976) 337-346.
  11. K.I. Noor, Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roum. Math. Pures Appl. 28 (8) (1983) 731-739.
  12. Ch. Pommerenke, Univalent Functions, Vandenhoeck und Ruprecht, Göttingen, 1975.
  13. R.K. Raina, J. Sokół, Fekete-Szegö problem for some starlike functions related to shell-like curves, Math. Slovaca 66 (2016) 135-140.
  14. V. Ravichandran, S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Acad. Sci. Paris, Ser. I 353 (6) (2015) 505-510.
  15. M. Raza, S.N. Malik, Upper bound of the third Hankel determinant for a class of analytic functions related with Lemniscate of Bernoulli, J. Inequal. Appl. 2013 (2013) Article 412.
  16. J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999) 111-116.
  17. J. Sokół, S. İlhan, H. Ö. Güney, Second Hankel determinant problem for several classes of analytic functions related to shell-like curves connected with Fibonacci numbers, TWMS Journal of Applied and Engineering Mathematics 8 (1a) (2018) 220-229.

About this Article

TITLE:
An Upper Bound for Third Hankel Determinant of Starlike Functions Related to Shell-like Curves Connected with Fibonacci Numbers

AUTHORS:
Janusz Sokół (1)
Sedat İlhan (2)
H. Özlem Güney (3)

AUTHORS AFFILIATIONS:
(1) Faculty of Mathematics and Natural Sciences, University of Rzeszów, POLAND
(2) Department of Mathematics, Faculty of Science, Dicle University, TURKEY
(3) Department of Mathematics, Faculty of Science, Dicle University, TURKEY

JOURNAL:
Journal of Mathematics and Applications
14/41

KEY WORDS AND PHRASES:
Analytic functions; Convex function; Fibonacci numbers; Hankel determinant; Shell-like curve; Starlike function

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/77

DOI:
10.7862/rf.2018.14

URL:
http://dx.doi.org/10.7862/rf.2018.14

RECEIVED:
2017-12-08

COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow

POLITECHNIKA RZESZOWSKA im. Ignacego Łukasiewicza; al. Powstańców Warszawy 12, 35-959 Rzeszów
tel.: +48 17 865 11 00, fax.: +48 17 854 12 60
Administrator serwisu: