Generalized von Neumann-Jordan constant and its relationship to the fixed point property
Generalized von Neumann-Jordan constant and its relationship to the fixed point property
Abstract We introduce a new geometric constant $C_{NJ}^{(p)}(X)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>J</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:math> for a Banach space X , called a generalized von Neumann-Jordan constant. Next, it is shown that $1\leq C_{NJ}^{(p)}(X)\leq2$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>≤</mml:mo> <mml:msubsup> …