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Midconvex functions in locally compact groups
Author(s):
A.
Chademan;
F.
Mirzapour
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2961-2968.
MSC (1991):
Primary 26A51;
Secondary 22A10
Posted:
June 17, 1999
MathSciNet review:
1610936
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Abstract:
The theorems of Bernstein-Doetsch, and Ostrowski, concerning the continuity of midconvex functions are extended to open subsets of locally compact and root-approximable topological groups.
References:
- [1]
- F. Bernstein and G. Doetsch, Zur Theorie der Konvexen Funktionen, Math. Ann. 76 (1915), 514-526.
- [2]
- H. Blumberg, On convex functions, Trans. Amer. Math. Soc. 20 (1919), 40-44.
- [3]
- N. Bourbaki, Topologie générale, chap. 3 et 4, 2-ième éd. (Actualités Scientifiques et Industrielles no. 1143), Hermann, Paris, (1960). MR 25:4021
- [4]
- N. Bourbaki, Espaces vectoriels topologiques, chap. 1 et 2, 2-ième éd. (Actualités Scientifiques et Industrielles no. 1198), Hermann, Paris, (1966).
- [5]
- A. Chademan, Sur les notions élémentaires de la théorie spectrale, Thèse de Doctorat 3-ième cycle, Univ. Paris VI, 1970.
- [6]
- A. Chademan and F. Mirzapour, Boundedness properties of midconvex functions in locally comact groups, (in Proc. of the 26-th AIMC, March 1995, published by the Iranian Math. Society and University of Kerman, Kerman, Iran), 1995, 59-63. CMP 98:07
- [7]
- R. Ger, Some remarks on convex functions, Fund. Math. 66(1970), 255-262. MR 40:7405
- [8]
- R. Ger,
 -convex functions in linear spaces, Aequationes Math. 11 (1974), 172-176. MR 50:10584 - [9]
- R. Ger and M. Kuczma, On the boundedness and continuity of convex functions and additive functions, Aequationes Math. 4(1970), 157-162. MR 41:8605
- [10]
- I.I. Hirschman and D.V. Widder, The convolution transform, Princeton University Press, Princeton, New Jersey, (1955). MR 17:479c
- [11]
- J. L. W. V. Jensen, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math. 30(1906), 175-193.
- [12]
- Z. Kominek, On additive and convex functionals, Rad. Mat. 3 (1987), 267-279. MR 89e:26029
- [13]
- Z. Kominek and M. Kuczma,, Theorems of Bernstein-Doetsch, Piccard and Mehdi and semilinear topology, Arch. Math. 52 (1989), 595-602. MR 90i:46017
- [14]
- M. Kuczma, An introduction to the theory of functional equations and inequations. Cauchy's equation and Jensen's inequality, PWN i Uniwersytest Slcaski, Warszawa, (1985). MR 86i:39008
- [15]
- M.R. Mehdi, On convex functions, J. Lond. Math. Soc. 39 (1964), 321-326. MR 28:5153
- [16]
- C.T. Ng and K. Nikodem, On approximately convex functions, Proc. Amer. Math. Soc. 118 (1993), 103-108. MR 93f:26006
- [17]
- A. Ostrowski, Uber die Funktionalgleichung der Exponentialfunktionen und verwande Funktionalgleichungen, Jahresber. Deut. Math. Ver., 38(1929), 54-62.
- [18]
- A.W. Roberts and D.A. Varberg, Convex functions, Academic Press, New York, (1973). MR 56:1201
- [19]
- W. Sierpinski, Sur les fonctions convexes mesurables; Fund. Math. 1 (1920), 125-129.
- [20]
- A. Weil, L' intégration dans les groupes topologiques et ses applications, 2-ième éd., (Actualités Scientifiques et Industrielles no. 1145), Hermann, Paris, (1965).
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Additional Information:
A.
Chademan
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, University of Tehran, Tehran, Iran
Email:
chademan@khayam.ut.ac.ir
F.
Mirzapour
Affiliation:
Department of Mathematics, University of Zanjan, Zanjan, Iran
DOI:
10.1090/S0002-9939-99-04907-2
PII:
S 0002-9939(99)04907-2
Keywords:
Midconvex functions,
locally compact groups,
Bernstein-Doetsch theorem,
Jensen's theorem,
Ostrowski's theorem
Received by editor(s):
December 12, 1996
Received by editor(s) in revised form:
January 1, 1998
Posted:
June 17, 1999
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1999,
American Mathematical Society
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