# ON A SUBCLASS OF CERTAIN STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

• Kamali, Muhammet ;
• Orhan, Halit
• Published : 2004.02.01
• 105 8

#### Abstract

A certain subclass $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ of starlike functions in the unit disk is introduced. The object of the present paper is to derive several interesting properties of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Coefficient inequalities, distortion theorems and closure theorems of functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are determined. Also we obtain radii of convexity for the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$. Furthermore, integral operators and modified Hadamard products of several functions belonging to the class $T_{\Omega}(n,\;p,\;\lambda,\;\alpha)$ are studied here.

#### References

1. Ann. Univ. Mariae Curie-Sklodowska Sect. v.A29 Convolutions of univalent functions with negative coefficients A.Schild;H.Silverman
2. Rend. Sem. Math. Univ. Padova v.77 A note on certain classes of starlike functions H.M.Srivastava;S.Owa;S.K.Chatterjea
3. Lecture Notes in Math. v.1013 Subclasses of univalent functions G.S.Salagean https://doi.org/10.1007/BFb0066543
4. Math. Japon v.36 no.3 On a subclass of certain starlike functions with negative coefficients O.Altintas
5. Comput. Math. Appl. v.30 no.2 Fractional calculus and certain starlike functions with negative coefficients O.Altintas;H.Irmak;H.M.Srivastava
6. Turkish J. Math. v.20 no.3 Certain classes of analytic and multivalent functions with negative coefficients M.K.Aouf;A.Shamandy;A.A.Attiyia
7. Appl. Math. Comput. v.145 no.2;3 On a subclass of certain convex functions with negative coefficients M.Kamali;S.Akbulut https://doi.org/10.1016/S0096-3003(02)00491-5
8. Proc. Amer. Math. Soc. v.51 Univalent functions with negative coefficients H.Silverman https://doi.org/10.1090/S0002-9939-1975-0369678-0

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