Bounds of the initial coefficient for sakaguchi function in the conical domain

Balaji S, B. Srutha Keerthi


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.

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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



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Copyright (c) 2019 Balaji S

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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