Coincidence of Nodes for Generalized Convex Functions
Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 317-320
Voir la notice de l'article provenant de la source Cambridge University Press
In a recent paper [1] I. B. Lazarevic announced an extension of results of L. Tornheim [2; Theorems 2 & 3] concerning points of contact between two distinct members of an n-parameter family and between a member of an n-parameter family and a corresponding convex function. In the proofs of these extensions [1; Theorems 3.1 & 3.2] use is made of Tornheim′s Convergence Theorem [2; Theorem 5]; however this theorem is not correctly applied in [1] since it requires distinct limiting nodes, and that hypothesis necessarily fails in the approach used in [1], In this note proofs of results more general than those in [1] are given independent of convergence theorems.
Mathsen, R. M. Coincidence of Nodes for Generalized Convex Functions. Canadian mathematical bulletin, Tome 23 (1980) no. 3, pp. 317-320. doi: 10.4153/CMB-1980-044-0
@article{10_4153_CMB_1980_044_0,
author = {Mathsen, R. M.},
title = {Coincidence of {Nodes} for {Generalized} {Convex} {Functions}},
journal = {Canadian mathematical bulletin},
pages = {317--320},
year = {1980},
volume = {23},
number = {3},
doi = {10.4153/CMB-1980-044-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-044-0/}
}
[1] 1. Lazarevic, LB., Some Properties of n -parameter Families of Functions, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 357-380 (1971), 101-106 MR47#8792. Google Scholar
[2] 2. Tornheim, L., On n-parameter families of functions and associated convex functions, Trans. Amer. Math. Soc. 69 (1950), 457-467. MR12#395. Google Scholar
[3] 3. Mathsen, R.M., k(n)-convex functions, Rocky Mountain Journal of Math. 2(1) (1972), 31-43. MR45#3651. Google Scholar
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