Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination | Zendy

Rosihan M. Ali | Zendy; Eun Ju Cho | Zendy; Kumar Jain | Zendy; V. Ravichandran | Zendy

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Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination

Author(s) -

Rosihan M. Ali,

Eun Ju Cho,

Kumar Jain,

V. Ravichandran

Publication year - 2012

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1203553a

Subject(s) - mathematics , convexity , subordination (linguistics) , convex function , radius , order (exchange) , mathematical analysis , regular polygon , class (philosophy) , pure mathematics , analytic function , combinatorics , geometry , linguistics , philosophy , computer security , finance , computer science , financial economics , economics , artificial intelligence

Several radii problems are considered for functions f(z) = z + a2z 2 + · · · with fixed second coeffcient a2. For 0 ≤ β < 1, sharp radius of starlikeness of order β for several subclasses of functions are obtained. Theseincludetheclassofparabolicstarlikefunctions, theclassofJanowskistarlikefunctions, and the class of strongly starlike functions. Sharp radius of convexity of order β for uniformly convex functions, and sharp radius of strong-starlikeness of order γ for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

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