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2001, br. 5, str. 95-101
Roughly d-convex functions on undirected tree networks
(naslov ne postoji na srpskom)
Str. Albac, Cluj-Napoca, Romania

e-adresadanielamarian@yahoo.com
Ključne reči: p-d-convex; b-d-convex; midpoint b-d-convex; γ-d-convex; lightly γ-d-convex; midpoint γ -d-convex; strictly γ -d-convex; strictly r-d-convexlike functions; tree networks
Sažetak
(ne postoji na srpskom)
In this paper we establish some properties of roughly d-convex functions on undirected tree networks. It is pointed out that these roughly d-convex functions have the following properties concerning the property of minimum each local minimum of a midpoint b-d-convex or lightly γ-d-convex functions is a global minimum, where a local with radius equal to the roughness degree. Since every p-d-convex and every γ -d-convex function is lightly γ -d convex, this conclusion holds for them, too. We also state weaker but sufficient conditions for roughly d-convex functions. We adopt the definition of network as metric space introduced by Dearing P.M. and Francis R.L. in 1974.
Reference
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Labbe, M. (1985) Essay in network location theory. Cahiers de Centre d'Etudes et de Recherche Oper, 27(1-2), 7-130
Marian, D. (1999) Generalized convex functions and mathematical analysis on networks. u: Research on Theory of Allure, Approximation, Convexivity and Optimization, Cluj-Napoca, 183-206
Phu, H.X. (1995) Six kinds of roughly convex functions. IWR, University of Heidelberg, Reprint 95-15
Phu, H.X. (1965) Strictly roughly convexlike functions. IWR, University of Heidelberg, Reprint 96-02
Phu, H.X. (1993) γ-subdifferential and γ-convexivity of functions on the real line. Applied Mathematics and Optimization, 27, 145-160
Phu, H.X. (1995) γ-subdifferential and γ-sonvexivity of functions on a normed space. Journal of Optimization Theory and Applications, 85, 649-676
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Phu, H.X., Hai, N.N., An, P.T. (1995) Piecewise constant roughly convex functions. Gottbus: Fakultat für Mathematik, Naturwissenschaften und Informatik, Technische Universität, Reprint M-09/1995
Popoviciu, E. (1972) Teoreme de medie din analiza matematică şi legătura lor cu teoria interpolării. Cluj-Napoca: Dacia
Sollner, B. (1991) Eigenschaften γ-grobconvexer Mengen und Funktionen. Diplomarbeit
Soltan, V.P., Soltan, P.S. (1979) d-convex functions. Docl. Akad. Nauk., SSSR, 249, 555-558
Soltan, V.P. (1984) Introduction to the axiomatic convexivity theory. Chisinau: Ştiinţa, Russian
 

O članku

jezik rada: engleski
vrsta rada: članak
DOI: 10.5937/MatMor0105095M
objavljen u SCIndeksu: 05.05.2008.

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