Hölder’s means and absolute normalized norms on R2

Abstract

Recently, Cui and Lu have introduced the constant H p (X) (p ∈ R) of a Banach space X by using Hölder's means. In this paper, we determine and estimate the new constant under the absolute normalized norms on R 2 by means of their corresponding continuous convex functions on [0, 1]. Furthermore, the exact values of the constant are calculated in some concrete Banach spaces. In particular, we calculate the precise values of the constants A 2 (X) and T(X) and the Gao constant E(X) in these concrete spaces.

On von Neumann-Jordan type constant and sufficient conditions for fixed points of multivalued nonexpansive mappings

“…Both the James constant J(X) and the von Neumann-Jordan constant C N J (X) play an important role in the description of various geometric structures. Therefore, many recent studies have focused on these constants (see [3,4,5,6,7,8,10,11,15,16,20,23,25,26]). S. Dhompongsa et al [5] introduced the Domínguez-Lorenzo condition ((DL)-condition, in short) which implies weak normal structure of a Banach space and the fixed point property for multivalued nonexpansive mappings.…”