Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Improved logarithmic-geometric mean inequality and its application232323261110ENL.ZouSchool of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, P.R. China.Journal Article20161022In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.http://bims.iranjournals.ir/article_1110_a2473c8ce3620a45bb9b80377280bcee.pdf