Convex functions of order n on undirected networks

Authors

  • Daniela Marian Cluj-Napoca, Romania

Abstract

In this paper we introduce the convex (nonconcave, polynomial, nonconvex, respective concave) functions of order \(n\) on undirected networks. We study some properties of them. Finally we frame these functions in allure theory introduced by E. Popoviciu (1983). We adopt the definition of network as metric space introduced by P. M. Dearing and R. L. Francis (1974).

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References

P. M. Dearing, R. L. Francis, A minimax location problem on a network, Transportation Science 8 (1974), 333-343, https://doi.org/10.1287/trsc.8.4.333

P. M. Dearing, R. L. Francis, T. J. Lowe, Convex location problems on tree networks, Oper. Res. 24 (1976), 628-634, https://doi.org/10.1287/opre.24.4.628

M. E. Iacob, Convexity, Approximation and Optimization on Networks, PhD dissertation, Univ. Babeş-Bolyai, Cluj-Napoca, 1997 (in Romanian).

M. Labeé, Essay in network location theory, Cahiers de Centre d'Etudes et Recherche Oper. 27 (1-2), (1985), 7-130.

D. Marian, Properties of the metric polynom of Lagrange type on undirected networks, Proceedings of the Conference on Analysis, Functional Equations, Approximation and Convexity, Cluj-Napoca, 15-16 October (1999), 152-159.

E. Popoviciu, Teoreme de medie din analiza matematică şi legătura lor cu teoria interpolării, Dacia, Cluj, 1972 (in Romanian).

E. Popoviciu, Sur certains propriétés des fonctions quasi-convexes (I), L'Analyse Numer. et la Theor. de l'Approx., 12, 2, (1983), 175-186.

T. Popoviciu, Sur quelques propiétés des fonctions d'une ou de deux variables réelles, Mathematica (Cluj) 8 (1933),1-85.

T. Popoviciu, Sur l'approximation des fonctions convexes d'ordre supérieur, Mathematica (Cluj) 10 (1934), 49-54.

T. Popoviciu, Notes sur les fonctions convexes d'ordre supérieur (I), Mathematica (Cluj) 12 (1936), 81-92.

T. Popoviciu, Notes sur les fonctions convexes d'ordre supérieur (II), Mathematica (Cluj) 12 (1936), 227-233.

T. Popoviciu, Introduction à la théorè des différences divisées, Bull. Math. Soc. Roumaine Sci. 42 (1940), 65-78.

T. Popoviciu, Les Fonctions Convexes, Herman, Actualités Scientifiques et Industrielles, Paris, 1945.

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Published

2000-08-01

How to Cite

Marian, D. (2000). Convex functions of order n on undirected networks. Rev. Anal. Numér. Théor. Approx., 29(2), 151–160. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2000-vol29-no2-art5

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