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- W2080468976 abstract "Let Ω k ⊂ C denote a domain, such that 1∈Ω k and ∂Ω k is a conic section, with eccentricity equal to 1/ k . In this paper authors introduce the class of k -uniformly convex functions k -UCV, with the property that the values of the expression 1+ zf ″( z )/ f ′( z ) lie inside the domain Ω k . Necessary and sufficient conditions for membership in k -UCV, as well as sharp growth and distortion theorems for k -uniformly convex functions are given. The obtained results generalize the concept of uniform convexity due to A.W. Goodman (Ann. Polon. Math. 56 (1991) 87–92)." @default.
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- W2080468976 date "1999-05-01" @default.
- W2080468976 modified "2023-10-03" @default.
- W2080468976 title "Conic regions and k-uniform convexity" @default.
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- W2080468976 doi "https://doi.org/10.1016/s0377-0427(99)00018-7" @default.
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