{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T05:27:23Z","timestamp":1772602043501,"version":"3.50.1"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>We continue to adopt notations and methods used in the papers illustrated by Yang (2009, 2010) to investigate the monotonicity properties of the ratio of mixed two-parameter homogeneous means. 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