{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:09:13Z","timestamp":1746803353693,"version":"3.40.5"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2017]]},"abstract":"<jats:p>A<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>value of a sequence<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>\u03c0<\/mml:mi><mml:mo>=<\/mml:mo><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msub><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>of elements of a finite metric space<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>is an element<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:math>for which<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:msubsup><mml:mo stretchy=\"false\">\u2211<\/mml:mo><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>=<\/mml:mo><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msubsup><mml:mrow><mml:msup><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>is minimum. The<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>\u2013function with domain the set of all finite sequences on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>and defined by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u03c0<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><mml:mo>=<\/mml:mo><mml:mo stretchy=\"false\">{<\/mml:mo><mml:mi>x<\/mml:mi><mml:mtext>:<\/mml:mtext><mml:mo>\u2009<\/mml:mo><mml:mo>\u2009<\/mml:mo><mml:mi>x<\/mml:mi><\/mml:math>is a<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>value of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mi>\u03c0<\/mml:mi><mml:mo stretchy=\"false\">}<\/mml:mo><\/mml:math>is called the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>\u2013function on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>d<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>. The<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M15\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M16\"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant=\"script\">l<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>\u2013functions on the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M17\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.<\/jats:p>","DOI":"10.1155\/2017\/8025616","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T21:03:06Z","timestamp":1483995786000},"page":"1-5","source":"Crossref","is-referenced-by-count":0,"title":["Axioms for Consensus Functions on the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-Cube"],"prefix":"10.1155","volume":"2017","author":[{"given":"C.","family":"Garcia-Martinez","sequence":"first","affiliation":[{"name":"Departamento de Ciencias B\u00e1sicas, Universidad Aut\u00f3ma Metropolitana Unidad Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, C.P. 02200 Ciudad de M\u00e9xico, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5770-6336","authenticated-orcid":true,"given":"F. R.","family":"McMorris","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA"},{"name":"Department of Mathematics, University of Louisville, Louisville, KY 40292, USA"}]},{"given":"O.","family":"Ortega","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Harold Washington College, Chicago, IL 60601, USA"}]},{"given":"R. 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