Optimal bounds for Neuman-Sándor mean in terms of the geometric convex combination of two Seiffert means

• Main Authors: Hua-Ying Huang, Nan Wang, Bo-Yong Long
• Format: Article
• Language: English
• Published: SpringerOpen 2016-01-01
• Series: Journal of Inequalities and Applications
• Subjects: Neuman-Sándor mean; the first Seiffert mean; the second Seiffert mean
• Online Access: http://link.springer.com/article/10.1186/s13660-015-0955-2

Abstract In this paper, we find the least value α and the greatest value β such that the double inequality P α ( a , b ) T 1 − α ( a , b ) < M ( a , b ) < P β ( a , b ) T 1 − β ( a , b ) $$P^{\alpha}(a,b)T^{1-\alpha}(a,b)< M(a,b)< P^{\beta}(a,b)T^{1-\beta}(a,b) $$ holds for all a , b > 0 $a,b>0$ with a ≠ b $a\neq b$ , where M ( a , b ) $M(a,b)$ , P ( a , b ) $P(a,b)$ , and T ( a , b ) $T(a,b)$ are the Neuman-Sándor, the first and second Seiffert means of two positive numbers a and b, respectively.