caa a22 4500 605508720 CHVBK 20210128100638.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00010-015-0344-4 doi (NATIONALLICENCE)springer-10.1007/s00010-015-0344-4 Berrone Lucio Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Laboratorio de Acústica y Electroacústica, Facultad de Ciencias Exactas, Ing. y Agrim., Universidad Nacional de Rosario, Riobamba 245 bis, 2000, Rosario, Argentina aut The Aumann functional equation for general weighting procedures [Elektronische Daten] [Lucio Berrone] The functional equation of composite type 1 $$M(M(x,M(x,y)),M(M(x,y),y))=M(x,y)$$ M ( M ( x , M ( x , y ) ) , M ( M ( x , y ) , y ) ) = M ( x , y ) arose in the course of the studies on the problem of extension and restriction of the number of arguments of a mean M performed by G. Aumann in the third decade of the past century. A solution to (1) in the analytic case was ulteriorly obtained by Aumann himself and remained as a noteworthy characterization of analytic quasiarithmetic means. An ample generalization of Eq.(1) which involves general weighting operators is considered in this paper. Under mild conditions on the regularity of the involved means, the general solution to this generalized equation is obtained for a particularly tractable class of weighting operators. Springer Basel, 2015 Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1051-1073 0001-9054 89:4<1051 2015 89 10 https://doi.org/10.1007/s00010-015-0344-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-015-0344-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Berrone Lucio Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Laboratorio de Acústica y Electroacústica, Facultad de Ciencias Exactas, Ing. y Agrim., Universidad Nacional de Rosario, Riobamba 245 bis, 2000, Rosario, Argentina aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/4(2015-08-01), 1051-1073 0001-9054 89:4<1051 2015 89 10