Geometric properties related to fixed point theory in some Banach function lattices (Q2761637)

The focus of the ``Handbook of metric fixed point theory'' is to present the major developments of metric fixed point theory. In this Chapter 12 of the handbook, the authors present in detail some important geometric properties of Banach function lattices, mainly in Orlicz spaces and Cesàro sequence spaces. The structure of the paper is as follows: 1. Orlicz spaces, 2. Normal structure, weak normal structure, weak sum property, sum property and uniform normal structure, 3. Uniform rotundity in every direction, 4. B-convexity and uniform monotonicity, 5. Nearly uniform convexity and nearly uniform smoothness, 6. WORTH and uniform nonsquareness, 7. Opial property and uniform Opial property in modular sequence spaces, 8. Garcia-Falset coefficient, 9. Cesàro sequence spaces, 10. WCSC, uniform Opial property, k-NUC and UNS for \(\text{ces}_p\).NEWLINENEWLINENEWLINEThe level of exposition is directed toward a wide audience, embracing students as well as established researchers.NEWLINENEWLINEFor the entire collection see [Zbl 0970.54001].