Strictly and Roughly Convexlike Functions

H.X. Phu
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H.X. Phu: Institute of Mathematics

Journal of Optimization Theory and Applications, 2003, vol. 117, issue 1, No 8, 139-156

Abstract: Abstract A function $$f:D \subseteq \mathbb{R}^n \to \mathbb{R}$$ is said to be strictly and roughly convexlike with respect to the roughness degree r > 0 (for short, strictly r-convexlike) provided that, for all x 0, x 1 ∈ D satisfying ||x 0 − x 1|| > r, there exists a λ ∈ ]0, 1[ such that $$f((1 - \lambda )x_0 + \lambda x_1 )

Keywords: Generalized convexity; strictly and roughly convexlike functions; strictly γ-convex functions (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/A:1023608624625

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