Bounds of the Initial Coefficient For Sakaguchi Function In The Conical Domain

Balaji S

Abstract


In this paper, we consider a new class of sakaguchi type functions which is defined by Ruscheweyh q-differential operator. We investigated of co-efficient inequalities and other interesting properties of this class.

Full Text:

PDF

References


N.I. Ahiezer, “Elements of theory of elliptic functions”, Moscow, 1970.

S. Hussain, S. Khan, M.A. Zaighum and M.Darus, “Certain subclass of analytic functions related with conic domains and associated with salagean q-differential operator”, AIMS Math.,vol.2, no. 4, pp. 622-634, 2017.

S.Hussain, S. Khan, M.A. Zaighum, M.Darus and Z.Shareef, “Coefficient Bounds for Certain Subclass of Biunivalent Functions Associated with Rucheweyh q-differential Operator”, J. Complex Anal., 2017 (2017).

W. Janowski, “Some extremal problems for certain families of analytic functions”, Ann. Polon.Math., vol. 28, pp. 297-326, 1973.

S. Kanas and A.Wisniowska, “Conic regions and k-uniform convexity”, J. Comput. Appl. Math.,vol. 105, pp. 327-336, 1999.

S. Kanas and A. Wisniowska, “Conic domains and starlike functions”, Rev. RoumaineMath.Pures Appl., vol. 45, pp. 647-657, 2000.

S.Kanas and D. Raducanu, “Some classes of analytic functions related to conic domains”, Math.slovaca, vol. 64, no. 5, pp. 1183-1196, 2014.

F.R. Keogh and E.P. Merkes, “A coefficient inequality for certain classes of analytic functions”, Proc. Amer. Math. Soc., vol. 20, pp. 8-12, 1969.

N. Khan, B. Khan, Q.Z. Ahmad and S.Ahmad, “Some Convolution properties of Multivalent Analytic Functions”,AIMS Math., vol. 2, no. 2, pp. 260-268, 2017.

W. Ma and D. Minda, A unified treatment of some special classes of univalent functions. In: Proc. of the Conference on Complex Analysis (Tianjin), 1992 (Z. Li, F.Y.Ren, L.Yang, S.Y. Zhang,eds.), Conf. Proc.Lecture Notes Anal., Int. Press, Massachusetts, vol 1, pp. 157-169, 1994.

K.I. Noor and S.N. Malik, “On coefficient inequalities of functions associated with conic domains”, Comput. Math. Appl., vol. 62, pp. 2209-2217, 2011.

K.I. Noor, J. Sokol and Q.Z. Ahmad, “Applications of conic type regions to subclasses of meromorphicunivalent functions with respect to symmetric points”, Rev. R. Acad. Cienc. Exactas Fs.Nat., Ser. A Mat.,vol. 111, pp. 947C958, 2017.

K.I. Noor, J. Sokol and Q.Z. Ahmad, “Applications of the differential operator to a class of meromorphic univalent functions”,J. Egyptian Math. Soc.,vol. 24, no. 2, pp. 181-186, 2016.

M. Nunokawa, S. Hussain, N.Khan and Q.Z. Ahmad, “A subclass of analytic functions related with conic domain”, J. Clas. Anal.,vol. 9, pp. 137-149, 2016.

W.Rogosinski, “On the coefficient of subordinate functions”, Proc. Lond. Math. Soc., vol. 48, pp. 48-82, 1943.

S.T. Rucheweyh, “New criteria for univalent functions”, Proc. Amer. Math. Soc., vol. 49, pp. 109-115, 1975.

H. Silverman, “Univalent functions with negative coefficient”, Proc. Amer. Math. Soc., vol. 51, pp. 109-116, 1975.

S. Shams, S. R. Kulkarni and J.M. Jahangiri, “Classes of uniformly starlike and convex functions”, Int. J. Math. Sci., vol. 55, pp. 2959-2961, 2004.

S. Khaan, S. Hussain, M.S. Zhaighum and M. Mumtaz Khan, “New subclass of analytic functions in conical domain associated with Rucheweyh q-differential operator”, IJAA, vol. 16, no. 2, pp. 239-253, 2018.

G. Saravanan, Muthunagai. K, “Coefficient Estimates and Fekete- Szegὅ Inequality for a Subclass of

Bi-Univalent Functions Defined by Symmetric Q-Derivative Operatorby Using Faber Polynomial Techniques” , PEN, Vol.6, No.1, June 2018, pp. 241~250.

N.P. Damodaran , SruthaKeerthi.B, “Coefficient bounds for a subclass of Sakaguchi type functions

using Chebyshev Polynomial”, PEN, Vol.6, No.1, June 2018, pp. 296-304.

P. Murugabharathi, B. SruthaKeerthi , “Designing Filter for Certain Subclasses ofAnalytic Univalent Functions”, PEN,Vol.6, No.1, June 2018, pp. 274~284




DOI: http://dx.doi.org/10.21533/pen.v7i3.601

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Balaji S

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License