ON k-UNIFORMLY ROTUND SPACES AND SPACES WITH PROPERTY k-UC

In a recent paper Shunmugaraj and Thota characterized uniform convexity in terms of property UC. In this paper we introduce a more general notion called property k-UC and characterize k-uniform rotundity in terms of property k-UC. We also obtain some results related to k-uniform rotundity and property k-UC. Some results obtained in this paper generalize some results recently obtained by Shunmugaraj and Thota as well as a result of Suzuki et al.