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Coefficients of multivalent symmetric functions of bounded boundary rotation

  • A. K. Mishra
  • M. Choudhury
Article

Abstract

In this paper the sharp coefficient estimate problem for the classesCp(β, m) andVp(k,m) of multivalent close-to-convex functions of order β and multivalent functions of bounded boundary rotation of at mostkπ, whose functions are given bym-fold symmetric gap series, have been discussed respectively for β≥1−p/m>0 andk≥2(m/p). Moreover, it is shown that every function inVp(k,m) arep-valent close-to-convex; hencep-valent; ifk<2 (1+m/p).

Key Words and phrases

m fold gap series p-valent close-to-convex functions of order β multivalent functions of bounded boundary rotation coefficient estimate etc 

AMS (MOS) Subject classifications

(1980) 30C45 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • A. K. Mishra
    • 1
    • 2
  • M. Choudhury
    • 1
    • 2
  1. 1.P. G. Department of MathematicsBerhampur UniversityBhanja BiharIndia
  2. 2.Department of MathematicsS.K.C.G. CollegeParalakhemundiIndia

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