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020 _a9781848821903
_9978-1-84882-190-3
024 7 _a10.1007/978-1-84882-190-3
_2doi
050 4 _aQA329-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.724
_223
100 1 _aChidume, Charles.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGeometric Properties of Banach Spaces and Nonlinear Iterations
_h[electronic resource] /
_cby Charles Chidume.
264 1 _aLondon :
_bSpringer London,
_c2009.
300 _aXVII, 326 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1965
505 0 _aSome Geometric Properties of Banach Spaces -- Smooth Spaces -- Duality Maps in Banach Spaces -- Inequalities in Uniformly Convex Spaces -- Inequalities in Uniformly Smooth Spaces -- Iterative Method for Fixed Points of Nonexpansive Mappings -- Hybrid Steepest Descent Method for Variational Inequalities -- Iterative Methods for Zeros of ? – Accretive-Type Operators -- Iteration Processes for Zeros of Generalized ? —Accretive Mappings -- An Example; Mann Iteration for Strictly Pseudo-contractive Mappings -- Approximation of Fixed Points of Lipschitz Pseudo-contractive Mappings -- Generalized Lipschitz Accretive and Pseudo-contractive Mappings -- Applications to Hammerstein Integral Equations -- Iterative Methods for Some Generalizations of Nonexpansive Maps -- Common Fixed Points for Finite Families of Nonexpansive Mappings -- Common Fixed Points for Countable Families of Nonexpansive Mappings -- Common Fixed Points for Families of Commuting Nonexpansive Mappings -- Finite Families of Lipschitz Pseudo-contractive and Accretive Mappings -- Generalized Lipschitz Pseudo-contractive and Accretive Mappings -- Finite Families of Non-self Asymptotically Nonexpansive Mappings -- Families of Total Asymptotically Nonexpansive Maps -- Common Fixed Points for One-parameter Nonexpansive Semigroup -- Single-valued Accretive Operators; Applications; Some Open Questions.
520 _aNonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent, incisive findings and interesting open-questions, this volume will prove useful for graduate students of mathematical analysis and will be a key-read for mathematicians with an interest in applications of geometric properties of Banach spaces, as well as specialists in nonlinear operator theory.
650 0 _aOperator theory.
650 0 _aGlobal analysis (Mathematics).
650 0 _aFunctional analysis.
650 0 _aMathematical optimization.
650 0 _aIntegral equations.
650 0 _aNumerical analysis.
650 1 4 _aOperator Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M12139
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
650 2 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26016
650 2 4 _aIntegral Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12090
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781848821934
776 0 8 _iPrinted edition:
_z9781848821897
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1965
856 4 0 _uhttps://doi.org/10.1007/978-1-84882-190-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9335
_d9335