Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 4 (2009), 77 -- 88## APPLICATIONS OF GENERALIZED RUSCHEWEYH DERIVATIVE TO UNIVALENT FUNCTIONS WITH FINITELY MANY COEFFICIENTS

## Abdul Rahman S. Juma and S. R. Kulkarni

Abstract. By making use of the generalized Ruscheweyh derivative, the authors investigate several interesting properties of certain subclasses of univalent functions having the formf(z) = z - Σ _{n=2..m}((1 - β) e_{n}) / ((1 - nβ + α(1-n)) B_{1}^{λ, μ}(n)) z^{n}- Σ_{k=m+1..∞}a_{k}z^{k}.2000 Mathematics Subject Classification:30C45

Keywords:Ruscheweyh derivative; Integral operator; Univalent function.

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Abdul Rahman S. Juma S. R. Kulkarni Department of Mathematics Department of Mathematics Al-Anbar University, Fergusson College, Ramadi, Iraq. Pune 411004, India e-mail: absa662004@yahoo.com e-mail: kulkarni_ferg@yahoo.com