The aim of this paper is twofold. First we show that the famous H¨ older inequality (which one, according to (10) should be called as the Rogers inequality) was discovered by Grolous (5) and Besso (3) about 10 years before Rogers. On the other hand, a result obtained by Lewent (9) leads to a new proof of the famous Ky Fan inequality (2). Related results are pointed out, too.