Browse > Article
http://dx.doi.org/10.5831/HMJ.2020.42.2.319

ON A CLASS OF q-BI-UNIVALENT FUNCTIONS OF COMPLEX ORDER RELATED TO SHELL-LIKE CURVES CONNECTED WITH THE FIBONACCI NUMBERS  

Ahuja, Om P. (Department of Mathematical Sciences, Kent State University)
Cetinkaya, Asena (Department of Mathematics and Computer Sciences, Istanbul Kultur University)
Bohra, Nisha (Sri Venkateswara College, University of Delhi)
Publication Information
Honam Mathematical Journal / v.42, no.2, 2020 , pp. 319-330 More about this Journal
Abstract
We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.
Keywords
Fibonacci numbers; shell-like curves; q-difference operator; bi-univalent function; Fekete-$Szeg{\ddot{o}}$;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Om P. Ahuja and A. Cetinkaya, Use of Quantum calculus approach in mathematical sciences and its role in Geometric Function Theory, AIP Conference Proceedings, 2095, 020001 (2019), 020001-1-020001-14.
2 K. M. Ball, "8: Fibonacci's Rabbits Revisited", Strange Curves, Counting Rabbits, and Other Mathematical Explorations, Princeton, NJ: Princeton University Press, 2003. ISBN 978-0-691-11321-0.
3 D. A. Brannan and J. G. Clunie, Aspects of contemporary complex analysis, Academic Press, London, 1980.
4 J. Dziok, R. K. Raina and J. Sokol, Certain results for a class of convex functions related to a shell-like curve connected with Fibonacci numbers, Comp. Math. Appl. 61 (2011), 2606-2613.
5 H. O. Guney, G. Murugusundaramoorthy and J. Sokol, Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers, Acta Univ. Sapientiae, Mathematica, 10 (2018), no. 1, 70-84.   DOI
6 J. Dziok, R. K. Raina and J. Sokol, On alpha-convex functions related to a shelllike curve connected with Fibonacci numbers, Appl. Math. Comp. 218 (2011), 996-1002.   DOI
7 G. Gasper and M. Rahman, Basic hypergeometric series, Cambridge University Press, 2004.
8 A. W. Goodman, Univalent functions, Volume I and II, Polygonal Pub. House, 1983.
9 M. E. H. Ismail, E. Merkes and D. Steyr, A generalization of starlike functions, Complex Variables Theory Appl. 14 (1990), no.1, 77-84.   DOI
10 F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46 (1909), no. 2, 253-281.   DOI
11 F. H. Jackson, q-difference equations, Amer. J. Math. 32 (1910), no. 4, 305-314.   DOI
12 V. Kac and P. Cheung, Quantum calculus, Springer-Verlag, New-York, 2002.
13 M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68.   DOI
14 J. Sokol, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis, 175 (1999), 111-116.
15 C. Pommerenke, Univalent Functions, Vandenhoeck, Ruprecht, Gottingen, 1975.
16 R. K. Raina and J. Sokol, Fekete-Szego problem for some starlike functions related to shell-like curves, Math. Slovaca, 66 (2016), 135-140.   DOI