Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means
In the article, we prove that the double inequalities align* &α_1T(a,b)+(1-α_1)A(a,b)<TD(a,b)<β_1T(a,b)+(1-β_1)A(a,b), &T^α_2 (a,b)A^1-α_2 (a,b)<TD(a,b)<T^β_2 (a,b)A^1-β_2 (a,b) align* hold for all \(a,b>0\) with \(a eq b\) if and only if \(α_1≤ 3/4\), \(β_1≥1\), \(α_2≤ 3/4\) and \(β_2≥ 1\), where \(A(a,b)\), \(TD(a,b)\) and \(T(a,b)\) are the arithmetic, Toader and second Seiffert means of \(a\) and \(b\), respectively. , number=3, journal=Communications in Mathematics and Applications, author=He, Zai-Yin and Jiang, Yue-Ping and Chu, Yu-Ming, year=2019, month=Sep., pages=561–570