Let \(E\) be a real normed space and consider the following semi-inner products \((-,-)_i\), \((-,-)_s\) given by \[ \begin{aligned}(x,y)_i &:= \lim_{t\to 0-} {|y+tx|^2-|y|^2\over 2t}\quad x,y\in E\\ (x,y)_s &:= \lim_{t\to 0_+} {|y+ tx|^2-|y|^2\over 2t}\quad x,y\in E.\end{aligned} \] The author proves: Theorem 3: Let \(E\) be a real Banach space. Then the following statements are equivalent: i) \(E\) is reflexive; ii) For every nonzero continuous linear functional \(f\) on \(E\) there exists at least one element \(u\) in \(E\), \(|u|=1\) so that the following interpolation \[ |f|(x,u)_i\leq |f|(x,u)_s\tag{1} \] for all \(x\) in \(E\), holds.