Additively decomposed quasiconvex functions.(English)Zbl 0594.26009
The authors give a new definition of the convexity index introduced in a recently published paper byG. Debreu andT. C. Koopmans [Math. Program. 24, 1-38 (1982;Zbl 0495.90063)]. By means of this definition they give then characterizations of the quasiconvexity of the function s defined on \(X_ 1\times X_ 2\times...\times X_ p\) by \[ s(x_ 1,x_ 2,...,x_ p)=f_ 1(x_ 1)+f_ 2(x_ 2)+...+f_ p(x_ p), \] where, for each \(i\in \{1,2,...,p\}\), \(X_ i\) is a non-empty open convex subset of \(R^{n_ i}\) and \(f_ i\) is a non-constant real- valued function on \(X_ i\).
Reviewer: W.W.Breckner
MSC:
| 26B25 | Convexity of real functions of several variables, generalizations |
| 90B30 | Production models |
| 91B16 | Utility theory |
Keywords:
quasiconvex functions;additive decomposability;utility theory;production theory;convexity indexCitations:
Zbl 0495.90063Cite
Full Text:DOI
References:
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