Helly-type theorems for roughly convex-like sets

Numerical Functional Analysis and Optimization

Volumn 28, Issue 5-6, 2007, Pages 553-558

  An, Phan Thanh ^a,b  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

^b ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

Generalized convexity; Helly's theorem; Rough convexlikeness; Set of constant width

Indexed keywords

COMPUTATIONAL GEOMETRY; PROBLEM SOLVING; SET THEORY;

GENERALIZED CONVEXITY; HELLY'S THEOREM; ROUGH CONVEXLIKENESS; SET OF CONSTANT WIDTH;

THEOREM PROVING;

EID: 34249068602     PISSN: 01630563     EISSN: 15322467     Source Type: Journal    
DOI: 10.1080/01630560701348426     Document Type: Article

References (13)

1. P.T. An and N.N. Hai (2004). δ-Convexity in normed linear spaces. Numer. Funct. Anal. Optimiz. 25:407-422.
2. E.O. Buchman and F.A. Valentine (1982). Any new Helly numbers? Am. Math. Monthly 89(6):370-375.
3. H.T. Croft, K.J. Falconer, and R.K. Guy (1991). Unsolved Problems in Geometry. Springer-Verlag, New York.
4. L. Danzer, B. Gruenbaum, and V. Klee (1963). Helly's theorem and its relatives. In Convexity. AMS Proc. Symp. Pure Math. 7, San Diego, pp. 63-72.
5. H.G. Eggleston (1958). Convexity. Cambridge University Press, Cambridge.
6. E. Helly (1923). Über Mengen konvexer Körper mit gemeinschaftlichen Punkten. Jahrb. Deut. Math. Verein 32:175-176.
7. T.C. Hu, V. Klee, and D. Larman (1989). Optimization of globally convex functions. SIAM J. Control Optimiz. 27:1026-1047.
8. V. Klee (1953). The critical set of a convex body. Am. J. Math. 75:178-188.
9. Z.A. Melzak (1960). A note on sets of constant width. Proc. Am. Math. Soc. 11 (3):493-497.
10. H.X. Phu (2003). Some geometrical properties of γ-convex sets. Numer. Fund. Anal. Optimiz. 24:303-309.
11. H.X. Phu and P.T. An (1999). Outer γ-convexity in normed spaces. Vietnam J. Math. 27:323-334.
12. J. Radon (1921). Mengen convexer Körper, die einen gemeinsaamen Punkt enthalten. Math. Ann. 83:113-115.
13. G.T. Sallee (1975). A Helly-type theorem for width. In The Geometry of Metric and Linear Spaces. Lecture Notes in Mathematics, Vol. 490. Springer-Verlag, Berlin.