A note on reflexivity and nonconvexity

作者：Marrero Isabel^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(18): 6890-6894.

DOI：10.1016/j.na.2011.07.011

• Best approximation
• Cantor property
• Condensing map
• Contractive map
• Fixed point
• Measure of noncompactness
• Measure of nonconvexity
• Reflexivity
• Strict convexity

In this short note we prove that a Banach space X is reflexive if, and only if, the Eisenfeld-Lakshmikantham measure of nonconvexity in X satisfies the Cantor property. Using this characterization, some results in best approximation and fixed point theory for reflexive Banach spaces are generalized by removing convexity requirements.

• 出版日期2011-12