On $lambda$-Pseudo Bi-Starlike Functions with Respect to Symmetric Points Associated to Shell-Like Curves


Download PDF

Authors: G. MURUGUSUNDARAMOORTHY, K. VIJAYA AND H. ÖZLEM GüNEY

DOI: 10.46793/KgJMat2101.103M

Abstract:

In this paper we define a new subclass λpseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3| for f ????????ℒs,Σλ(α,˜p (z)). Further we determine the Fekete-Szegö result for the function class ????????ℒs,Σλ(α,˜p (z)) and for special cases, corollaries are stated which some of them are new and have not been studied so far.

Keywords:

Analytic functions, bi-univalent, shell-like curve, Fibonacci numbers, starlike functions.

References:

[1]    K. O. Babalola, On λpseudo-starlike functions, J. Class. Anal. 3(2) (2013), 137–147.

[2]    D. A. Brannan, J. Clunie and W. E. Kirwan, Coefficient estimates for a class of star-like functions, Canad. J. Math. 22 (1970), 476–485.

[3]   D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31(2) (1986), 70–77.

[4]    P. L. Duren, Univalent functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1983.

[5]    S. S. Eker and B. Seker, On λ-pseudo bi-starlike and λ-pseudo bi-convex functions with respect to symmetrical points, Tbilisi Math. J. 11(1) (2018), 49–57.

[6]    R. Jurasiska and J. Stankiewicz, Coefficients in some classes defined by subordination to multivalent majorants, in: Proceedings of Conference on Complex Analysis, Bielsko-Biala, 2001, Ann. Polon. Math. 80 (2003), 163–170.

[7]   J. Dziok, R. K. Raina and J. Sokół, On α-convex functions related to a shell-like curve connected with Fibonacci numbers, Appl. Math. Comp. 218 (2011), 996–1002.

[8]   M. Fekete and G. Szegö, Eine Bemerkung über ungerade schlichte Functionen, J. Lond. Math. Soc. 8 (1933), 85–89.

[9]    W. Ma and D. Minda, A Unified treatment of some special cases of univalent functions, in: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, International Press, Cambridge, USA, 157–169.

[10]    S. S. Miller and P. T. Mocanu, Differential Subordinations Theory and Applications, Series of Monographs and Text Books in Pure and Applied Mathematics 225, Marcel Dekker, New York, 2000.

[11]    M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68.

[12]    Ch. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.

[13]    R. K. Raina and J. Sokół, Fekete-Szegö problem for some starlike functions related to shell-like curves, Math. Slovaca 66 (2016), 135–140.

[14]    J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999), 111–116.

[15]    J. Sokół, On some subclass of strongly starlike functions, Demonstr. Math. 31(1) (1998), 81–86

[16]    J. Sokół and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Folia Scient. Univ. Tech. Resoviensis 147 (1996), 101–105

[17]    H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23(10) (2010), 1188–1192.

[18]    Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, Coefficinet estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), 990–994.

[19]    X-F. Li and A-P Wang, Two new subclasses of bi-univalent functions, International Mathematical Forum 7(30) (2012), 1495–1504.

[20]    P. Zaprawa, On the Fekete-Szegö problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin 21(10) (2014),169–178.