We first prove characterizations of -uniform convexity and -uniform smoothness. We next give a formulation on absolute normalized norms on . Using these, we present some examples of Banach spaces. One of them is a uniformly convex Banach space which is not -uniformly convex.
Tomonari Suzuki. "-Uniform Convexity and -Uniform Smoothness of Absolute Normalized Norms on ." Abstr. Appl. Anal. 2014 (SI25) 1 - 9, 2014. https://doi.org/10.1155/2014/746309