Yasuji Takahashi

Some Recent Results on Geometric Constants of Banach Spaces

We shall first present a unifying view of a sequence of results concerning the relation between the von Neumann‐Jordan constant CNJ(X) and James constant J(X) of a Banach space X. Secondly by using the new constant A(X) introduced by Takahashi and Kato [10], we shall strengthen some previous results, which yields a simple proof of the inequality CNJ(X)≤J(X) in [9].We shall first present a unifying view of a sequence of results concerning the relation between the von Neumann‐Jordan constant CNJ(X) and James constant J(X) of a Banach space X. Secondly by using the new constant A(X) introduced by Takahashi and Kato [10], we shall strengthen some previous results, which yields a simple proof of the inequality CNJ(X)≤J(X) in [9].

Convex sets and inequalities

We consider a natural correspondence between a family of inequalities and a closed convex set. As an application, we give new types of power mean inequalities and the Hölder-type inequalities.