Folgmann, G., Uber Verallgemeinerung konvexer Funktionen in linearen Raumen. Diss.(A), PH Halle, 1974. Home/Search Document Not in Database Summary Related Articles |
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On Modifications of the Standard Embedding in Nonlinear.. - Noubiap (1997) (1 citation) (Correct)
....(B) OE is quasiconvex on K if and only if one of the following conditions is satisfied: 1) x 1 ; x 2 2 K OE(x 2 ) OE(x 1 ) DOE(x 1 ) x 2 Gamma x 1 ) 0: 2) x 1 ; x 2 2 K OE(x 2 ) OE(x 1 ) DOE(x 1 ) x 2 Gamma x 1 ) 0: Proof: A) obvious. B) cf. [8]. Remark A.3 (1) Let K ae IR n be open and convex and OE 2 C 1 (K; IR) Then it holds: OE convex auf K = OE pseudoconvex auf K = OE quasiconvex auf K: 2) From the quasiconvexity (and pseudoconvexity respectively ) of the funktions OE 1 and OE 2 not follows generally the quasiconvexity ....
Folgmann, G., Uber Verallgemeinerung konvexer Funktionen in linearen Raumen. Diss.(A), PH Halle, 1974.
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