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Coincidence of Nodes for Generalized Convex Functions

Published online by Cambridge University Press:  20 November 2018

R. M. Mathsen
R. M. Mathsen*
Affiliation:
Department of Mathematics North Dakota State University Fargo, North Dakota 58102 and University of Alberta Edmonton, Alberta T6G 2G1
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 3 , 01 September 1980 , pp. 317 - 320
Copyright
Copyright © Canadian Mathematical Society 1980

References

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. 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. Mathsen, R.M., k(n)-convex functions, Rocky Mountain Journal of Math. 2(1) (1972), 31-43. MR45#3651.Google Scholar