Abstract
In this paper the sharp coefficient estimate problem for the classesC p(β, m) andV p(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 inV p(k,m) arep-valent close-to-convex; hencep-valent; ifk<2 (1+m/p).
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The research of the first author was supported by UGC New Delhi Major Research Project Grant No F-8-2/92 (SR-I), D 9.6.93.
The research was done while the second author visited Berhampuv University from S.K.C.G. College, Paralakemundi under U.G.C. New Delhi, Teacher Fellowship Scheme, Grant No F. 9-22/92 (CD-4) D 25.10.1993.
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Mishra, A.K., Choudhury, M. Coefficients of multivalent symmetric functions of bounded boundary rotation. Rend. Circ. Mat. Palermo 43, 403–412 (1994). https://doi.org/10.1007/BF02844251
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DOI: https://doi.org/10.1007/BF02844251
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