New inequalities for the function $y=t\ln t$

Abstract

The main aim of this note, which can be viewed as a certain addendum to the paper \cite{2020}, is to propose several new inequalities for the function $y=t\ln t.$ We consider the local behaviour of this function near the point $t=1,$ as well as the global behaviour of this function on the intervals $[1,\infty )$ and $(0,1].$