An alternative proof of a harmonic mean inequality for Nielsen’s beta function

Abstract

Abstract In this short note, an alternative proof of a harmonic mean inequality involving Nielsen’s beta function is provided. This inequality was first posed as a conjecture by Nantomah [Bull. Int. Math. Virtual Inst. 9 (2019) 263–269] and subsequently proved by Matejı́čka [Probl. Anal. Issues Anal. 8(26) (2019) 105–111]. The present proof is more compact and relatively simple.