An Introduction to Metric Spaces and Fixed Point Theory
Presents up-to-date Banach space results.
* Features an extensive bibliography for outside reading.
* Provides detailed exercises that elucidate more introductory material.
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assume assumption Axiom of Choice Banach lattice Banach space bounded closed convex bounded metric space bounded sequence Brouwer’s Theorem Cauchy sequence Chapter closed balls closed convex subset compact convex subset complete metric space continuous mapping contraction mapping contradiction converges weakly convex subset countable cov(A Deﬁnition denote diam(D element example Exercise exists fact family of closed ﬁnite-dimensional ﬁnitely representable ﬁrst ﬁxed point ﬁxed point property ﬁxed point set ﬁxed point theorem function f hence hyperconvex metric space hyperconvex spaces implies induction integer intersection isometric let f limsup mapping f metrically convex n—voo nonempty closed nonexpansive mappings nonexpansive retract norm normal structure Proposition proves real numbers reﬂexive result satisﬁes Schauder basis Show space and let space and suppose subspace super-reﬂexive topological space triangle inequality ultrametric space ultranet uniformly convex unique ﬁxed point weak Zorn’s Lemma