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Note on certain inequalities for Neuman means

Note on certain inequalities for Neuman means

Abstract In this paper, we give the explicit formulas for the Neuman means <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>H</mml:mi> <mml:mi>A</mml:mi> </mml:mrow> </mml:msub> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>N</mml:mi> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> …