Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME APPLICATIONS AND PROPERTIES OF GENERALIZED FRACTIONAL CALCULUS OPERATORS TO A SUBCLASS OF ANALYTIC AND MULTIVALENT FUNCTIONS

  • Lee, S.K. (Department of Mathematics, Gyeongsang National University) ;
  • Khairnar, S.M. (Department of Mathematics, Maharashtra Academy of Engineering) ;
  • More, Meena (Department of Mathematics, Maharashtra Academy of Engineering)
  • Received : 2008.11.03
  • Published : 20090600
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Abstract

In this paper we introduce a new subclass $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ of analytic and multivalent functions with negative coefficients using fractional calculus operators. Connections to the well known and some new subclasses are discussed. A necessary and sufficient condition for a function to be in $K_{\mu}^{\lambda},{\phi},{\eta}(n;{\rho};{\alpha})$ is obtained. Several distortion inequalities involving fractional integral and fractional derivative operators are also presented. We also give results for radius of starlikeness, convexity and close-to-convexity and inclusion property for functions in the subclass. Modified Hadamard product, application of class preserving integral operator and other interesting properties are also discussed.

Keywords

References

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