Author | Toledano, J. M. Ayerbe. author |
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Title | Measures of Noncompactness in Metric Fixed Point Theory [electronic resource] / by J. M. Ayerbe Toledano, T. Domรญnguez Benavides, G. Lรณpez Acedo |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8920-9 |
Descript | VII, 216 p. online resource |
I The fixed point theorems of Brouwer and Schauder -- 1 The fixed point theorem of Brouwer and applications -- 2 The fixed point theorem of Schauder and applications -- II Measures of noncompactness -- 1 The general notion of a measure of noncompactness -- 2 The Kuratowski and Hausdorff measures of noncompactness -- 3 The separation measure of noncompactness -- 4 Measures of noncompactness in Banach sequences spaces -- 5 Theorem of Darbo and Sadovskii and applications -- III Minimal sets for a measure of noncompactness -- 1 รธ-minimal sets -- 2 Minimalizable measures of noncompactness -- IV Convexity and smoothness -- 1 Strict convexity and smoothness -- 2 k-uniform convexity -- 3 k-uniform smoothness -- V Nearly uniform convexity and nearly uniform smoothness -- 1 Nearly uniformly convex Banach spaces -- 2 Nearly uniformly smooth Banach spaces -- 3 Uniform Opial condition -- VI Fixed points for nonexpansive mappings and normal structure -- 1 Existence of fixed points for nonexpansive mappings: Kirkโs theorem -- 2 The coefficient N(X) and its connection with uniform convexity -- 3 The weakly convergent sequence coefficient -- 4 Uniform smoothness, near uniform convexity and normal structure -- 5 Normal structure in direct sum spaces -- 6 Computation of the normal structure coefficients in Lp-spaces -- VII Fixed point theorems in the absence of normal structure -- 1 Goebel-Karlovitzโs lemma and Linโs lemma -- 2 The coefficient M(X) and the fixed point property -- VIII Uniformly Lipschitzian mappings -- 1 Lifshitz characteristic and fixed points -- 2 Connections between the Lifshitz characteristic and certain geometric coefficients -- 3 The normal structure coefficient and fixed points -- IX Asymptotically regular mappings -- 1 A fixed point theorem for asymptotically regular mappings -- 2 Connections between the ?-characteristic and some other geometric coefficients -- 3 The weakly convergent sequence coefficient and fixed points -- X Packing rates and รธ-contractiveness constants -- 1 Comparable measures of noncompactness -- 2 Packing rates of a metric space -- 3 Connections between the packing rates and the normal structure coefficients -- 4 Packing rates in lp-spaces -- 5 Packing rates in Lpspaces -- 6 Packing rates in direct sum spaces -- References -- List of Symbols and Notations