Generalized Cauchy means
dc.creator | Berrone, Lucio Renato | |
dc.date.accessioned | 2017-01-17T14:02:33Z | |
dc.date.accessioned | 2018-11-06T13:45:21Z | |
dc.date.available | 2017-01-17T14:02:33Z | |
dc.date.available | 2018-11-06T13:45:21Z | |
dc.date.created | 2017-01-17T14:02:33Z | |
dc.date.issued | 2015-01 | |
dc.identifier | Berrone, Lucio Renato; Generalized Cauchy means; Springer; Aequationes Mathematicae; 90; 2; 1-2015; 307-328 | |
dc.identifier | 0001-9054 | |
dc.identifier | http://hdl.handle.net/11336/11457 | |
dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/1878974 | |
dc.description.abstract | Given two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem. | |
dc.language | eng | |
dc.publisher | Springer | |
dc.relation | info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00010-015-0341-7 | |
dc.relation | info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00010-015-0341-7 | |
dc.rights | https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.subject | Cauchy means | |
dc.subject | Iteration of operators | |
dc.subject | Fixed points | |
dc.title | Generalized Cauchy means | |
dc.type | Artículos de revistas | |
dc.type | Artículos de revistas | |
dc.type | Artículos de revistas |