Optimal bounds for the Neuman-Sándor mean in terms of the first Seiffert and quadratic means
Optimal bounds for the Neuman-Sándor mean in terms of the first Seiffert and quadratic means
Abstract In this paper, we find the least value α and the greatest value β such that the double inequality <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>P</mml:mi> <mml:mi>α</mml:mi> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>)</mml:mo> <mml:msup> <mml:mi>Q</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>α</mml:mi> </mml:mrow> </mml:msup> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>)</mml:mo> <mml:mo><</mml:mo> <mml:mi>M</mml:mi> <mml:mo>(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> …