Titlebook: Handbook of Metric Fixed Point Theory; William A. Kirk,Brailey Sims Book 2001 Springer Science+Business Media Dordrecht 2001 banach spaces

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Classical Theory of Nonexpansive Mappings, an abstract metric space is all that is needed to define the concept. At the same time, the more interesting results seem to require some notion of topology; more specifically a topology which assures that closed metric balls are compact. This is not a serious limitation, however, because many spac

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Geometrical Background of Metric Fixed Point Theory,ay key roles in metric fixed point problems. In this text we discuss the most basic of these geometrical properties. Since many fixed point results have a quantitative character, we place special emphasis on the scaling coefficients and functions corresponding to the properties considered. The mater

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,Renormings of ℓ, and , , and Fixed Point Properties,ed point property. Geometric conditions such as uniform rotundity, uniform smoothness, or normal structure together with reflexivity are sufficient to imply the fixed point property. Each of these conditions also implies (or assumes in the last case) that the Banach space is reflexive.

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Nonexpansive Mappings: Boundary/Inwardness Conditions and Local Theory,ngs, particularly to mappings satisfying local contractive and pseudocontractive assumptions. At the same time these conditions often enable one to relax the assumption that the mapping takes values in its own domain.

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Introduction to Hyperconvex Spaces,.e. it is a non-expansive retract of any metric space in which it is isometrically embedded. The corresponding linear theory is well developed and associated with the names of Gleason, Goodner, Kelley and Nachbin (see for instance [19, 29, 42, 46]). The nonlinear theory is still developing. The rece

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Fixed Points of Holomorphic Mappings: A Metric Approach,aid to be . in .. if it is Fréchet differentiable at each point of ... If .. and .. are domains in .. and .., respectively, then .(.., ..) will denote the family of all holomorphic mappings from .. into ...

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