Convex functions and the Hadamard inequality

Alfonso G. Azpeitia

Published

1994-01-01

Convex functions and the Hadamard inequality

Keywords:

Convex and concave functions, arithmetic means, convexity inequalities (es)

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Authors

Alfonso G. Azpeitia University of Massachusetts

Abstract (en)

The Hadamard inequality is proven without resorting to any properties of the derivative. Only the convexity of the function in a closed interval is needed. Furthermore, if the existence of the integral is assumed, then the convexity requirement is weakened to convexity in the sense of Jensen. Both the Hadamard inequality and a corresponding upper bound are generalized for integrals of the Stieljes type.

How to Cite

APA

Azpeitia, A. G. (1994). Convex functions and the Hadamard inequality. Revista Colombiana de Matemáticas, 28(1), 7–12. https://revistas.unal.edu.co/index.php/recolma/article/view/33459

ACM

[1]

Azpeitia, A.G. 1994. Convex functions and the Hadamard inequality. Revista Colombiana de Matemáticas. 28, 1 (Jan. 1994), 7–12.

ACS

(1)

Azpeitia, A. G. Convex functions and the Hadamard inequality. rev.colomb.mat 1994, 28, 7-12.

ABNT

AZPEITIA, A. G. Convex functions and the Hadamard inequality. Revista Colombiana de Matemáticas, [S. l.], v. 28, n. 1, p. 7–12, 1994. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/33459. Acesso em: 2 feb. 2025.

Chicago

Azpeitia, Alfonso G. 1994. “Convex functions and the Hadamard inequality”. Revista Colombiana De Matemáticas 28 (1):7-12. https://revistas.unal.edu.co/index.php/recolma/article/view/33459.

Harvard

Azpeitia, A. G. (1994) “Convex functions and the Hadamard inequality”, Revista Colombiana de Matemáticas, 28(1), pp. 7–12. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/33459 (Accessed: 2 February 2025).

IEEE

[1]

A. G. Azpeitia, “Convex functions and the Hadamard inequality”, rev.colomb.mat, vol. 28, no. 1, pp. 7–12, Jan. 1994.

MLA

Azpeitia, A. G. “Convex functions and the Hadamard inequality”. Revista Colombiana de Matemáticas, vol. 28, no. 1, Jan. 1994, pp. 7-12, https://revistas.unal.edu.co/index.php/recolma/article/view/33459.

Turabian

Azpeitia, Alfonso G. “Convex functions and the Hadamard inequality”. Revista Colombiana de Matemáticas 28, no. 1 (January 1, 1994): 7–12. Accessed February 2, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/33459.

Vancouver

1.

Azpeitia AG. Convex functions and the Hadamard inequality. rev.colomb.mat [Internet]. 1994 Jan. 1 [cited 2025 Feb. 2];28(1):7-12. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/33459