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

Abstract

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 ) 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.

Keywords

• Neuman-Sándor mean
• the first Seiffert mean
• the second Seiffert mean