Uniform rotundity of Orlicz function spaces equipped with the ‐Amemiya norm

Necessary and sufficient conditions for uniform rotundity of Orlicz function spaces equipped with the p‐Amemiya norm are presented. The obtained results unify, complete and widen the characterization of uniform rotundity of Orlicz spaces. In the case of the ∞‐Amemiya (i.e. the Luxemburg) norm or the 1‐Amemiya (i.e. the Orlicz) norm, these results were known earlier. Some connections with the fixed point theory and the best approximation theory are presented.