The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some suffcient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper signicantly generalize and improve many known results in the recent literature.