This article is cited in 1 paper

On two new means of two arguments III

J. Sándor^a, B. A. Bhayo<sup>b

a</sup> Babeş-Bolyai University, Str. Kogalniceanu nr. 1, 400084 Cluj-Napoca, Romania
^b Sukkur IBA University, Sindh, Pakistan

Abstract: In this paper we establish two sided inequalities for the following two new means
$$ X=X(a,b)=Ae^{G/P-1},\qquad Y=Y(a,b)=Ge^{L/A-1}, $$
where $A$, $G$, $L$ and $P$ are the arithmetic, geometric, logarithmic, and Seiffert means, respectively. As an application, we refine many other well known inequalities involving the identric mean $I$ and the logarithmic mean $L$.

Keywords: inequalities; means of two arguments; identric mean; logarithmic mean.

UDC: 517.16

MSC: 26D05, 26D15, 26D99

Received: 21.11.2017
Revised: 28.02.2018
Accepted: 28.02.2018

Language: English

DOI: 10.15393/j3.art.2018.4590

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