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Measures of Noncompactness in Metric Fixed Point Theory (Hardcover) Loot Price: R2,633
Discovery Miles 26 330
Measures of Noncompactness in Metric Fixed Point Theory (Hardcover): J. M Ayerbe Toledano, Etc, T Dom inguez Benavides, G L...

Measures of Noncompactness in Metric Fixed Point Theory (Hardcover)

J. M Ayerbe Toledano, Etc, T Dom inguez Benavides, G L opez Acedo

Series: Operator Theory: Advances and Applications, v. 99

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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 o-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: Kirk's 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-Karlovitz's lemma and Lin's 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 o-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.

General

Imprint: Birkhauser Verlag AG
Country of origin: Switzerland
Series: Operator Theory: Advances and Applications, v. 99
Release date: September 1997
First published: November 1997
Authors: J. M Ayerbe Toledano • Etc • T Dom inguez Benavides • G L opez Acedo
Dimensions: 235 x 165mm (L x W)
Format: Hardcover
Pages: 224
ISBN-13: 978-3-7643-5794-8
Categories: Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
Books > Science & Mathematics > Mathematics > Geometry > General
Books > Science & Mathematics > Mathematics > Topology > General
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LSN: 3-7643-5794-0
Barcode: 9783764357948

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