In this chapter we consider the class of contractive mappings and show that a typical nonexpansive mapping (in the sense of Baire’s categories) is contractive. We also study nonexpansive mappings which are contractive with respect to a given subset of their domain and establish fixed point and convergence theorems for certain mappings of contractive type which take a closed subset of a complete metric space X into X. We study well-posedness of fixed point problems and construct important examples of nonexpansive mappings. In particular, we construct a contractive self-mapping of a closed interval such that none of its powers is a strict contraction and a nonexpansive mapping with nonuniformly convergent powers.
- 65.Goebel, K. (2004). Concise course on fixed point theory. Yokohama: Yokohama Publishers. Google Scholar
- 139.Reich, S., & Zaslavski, A. J. (2001). Far East Journal of Mathematical Sciences, Special Volume(Part III), 393–401. Google Scholar