Generalized Convexity and Inequalities
| dc.creator | Anderson, G. D. | |
| dc.creator | Vamanamurthy, M. K. | |
| dc.creator | Vuorinen, M. | |
| dc.date | 2007-01-09 | |
| dc.date.accessioned | 2026-07-07T09:37:52Z | |
| dc.date.available | 2026-07-07T09:37:52Z | |
| dc.description | Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701262 | |
| dc.identifier | http://arxiv.org/abs/math/0701262 | |
| dc.identifier | J. Math. Anal. Appl. 335 (2007), 1294-1308 | |
| dc.identifier | doi:10.1016/j.jmaa.2007.02.016 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160611 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 33C05; 33C20 (Primary); 26A51 (Secondary) | |
| dc.title | Generalized Convexity and Inequalities | |
| dc.type | text |