A geometrical constant and normal normal structure in Banach Spaces.

Recently, we introduced a new coefficient as a generalization of the modulus of smoothness and Pythagorean modulus such as J , ( t). In this paper, We can compute the constant J , (1) under the absolute normalized norms on ℝ by means of their corresponding continuous convex functions on [0, 1]. Moreover, some sufficient conditions which imply uniform normal structure are presented. 2000 Mathematics Subject Classification: 46B20. [ABSTRACT FROM AUTHOR]