Multiplicative properties of real functions with applications to classical functions

被引：1

作者：

Finol C.E. ^{[1
]}

Wójtowicz M. ^{[2
]}

机构：

[1] Departamento de Matemática, Facultad de Ciencias, Universidad Central de Venezuela, Caracas 1040-A

[2] Institute of Mathematics, Pedagogical University, PL-65-069 Zielona Góra

来源：

aequationes mathematicae | 2000年 / 59卷 / 1期

关键词：

Classical functions; Euler gamma function; log function; Functions: Geometrically convex; geometrically concave; submultiplicative; supermultiplicative; monotonic; Riemann zeta function;

D O I：

10.1007/PL00000120

中图分类号：

学科分类号：

摘要：

From the characterisation of geometrically convex and geometrically concave functions defined on (0, A] or [A, ∞) with A > 0, by means of their multiplicative conditions, we obtain unified proofs of some known and new inequalities. Functions of class C2 and strictly increasing on (a, b) fulfil some kind of supermultiplicativity and superadditivity. We have obtained a new constant determining the intervals of sub- and supermultiplicativity for the log function. © Birkhäuser Verlag, Basel, 2000.

引用

页码：134 / 149

页数：15

共 26 条

[1]

Bishop E.A., Holomorphic completion, analytic continuation, and the interpolation of seminorms, Ann. Math., 78, pp. 468-500, (1963)

[2]

Cooper R., The converses of the Cauchy-Hölder inequality and the solutions of the inequality g(x + y) ≤ g(x) + g(y), Proc. London Math. Soc., 26, pp. 285-291, (1927)

[3]

Finol C.E., On dilation functions and some applications, Publications Math., 33, pp. 307-322, (1986)

[4]

Finol C.E., Maligranda L., On a decomposition of some functions, Commentationes Math. (Prace Mat.), 30, pp. 285-291, (1991)

[5]

Gowers W.T., A solution to Banach's hyperplane problem, Bull. London Math. Soc., 26, pp. 523-530, (1994)

[6]

Gronau D., Selected topics on functional equations, Functional Analysis, IV, pp. 63-84, (1993)

[7]

Gronau D., Matkowski J., Geometrical convexity and generalization of the Bohr-Mollerup theorem on the gamma function, Math. Pannon., 4, pp. 153-160, (1993)

[8]

Gronau D., Matkowski J., Geometrically convex solutions of certain difference equations and generalized Bohr-Mollerup type theorems, Results Math., 26, pp. 290-297, (1994)

[9]

Gustavsson J., Maligranda L., Peetre J., A submultiplicative function, Indag. Math., 51, pp. 435-442, (1989)

[10]

Hardy G.A., Littlewood J.E., Polya G., Inequalities, (1934)

← 1 2 3 →