LEADER 05855nam 22008295 450 001 996466526203316 005 20200706112023.0 010 $a1-84882-190-5 024 7 $a10.1007/978-1-84882-190-3 035 $a(CKB)1000000000546259 035 $a(SSID)ssj0000317943 035 $a(PQKBManifestationID)11245545 035 $a(PQKBTitleCode)TC0000317943 035 $a(PQKBWorkID)10307696 035 $a(PQKB)11700493 035 $a(DE-He213)978-1-84882-190-3 035 $a(MiAaPQ)EBC3063832 035 $a(PPN)132867214 035 $a(EXLCZ)991000000000546259 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aGeometric Properties of Banach Spaces and Nonlinear Iterations$b[electronic resource] /$fby Charles Chidume 205 $a1st ed. 2009. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2009. 215 $a1 online resource (XVII, 326 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1965 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-84882-189-1 320 $aIncludes bibliographical references (p. 301-324) and index. 327 $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. 330 $aNonlinear functional analysis and applications is an area of study that has provided fascination for many mathematicians across the world. This monograph delves specifically into the topic of the geometric properties of Banach spaces and nonlinear iterations, a subject of extensive research over the past thirty years. Chapters 1 to 5 develop materials on convexity and smoothness of Banach spaces, associated moduli and connections with duality maps. Key results obtained are summarized at the end of each chapter for easy reference. Chapters 6 to 23 deal with an in-depth, comprehensive and up-to-date coverage of the main ideas, concepts and results on iterative algorithms for the approximation of fixed points of nonlinear nonexpansive and pseudo-contractive-type mappings. This includes detailed workings on solutions of variational inequality problems, solutions of Hammerstein integral equations, and common fixed points (and common zeros) of families of nonlinear mappings. Carefully referenced and full of recent, incisive findings and interesting open-questions, this volume will prove useful for graduate students of mathematical analysis and will be a key-read for mathematicians with an interest in applications of geometric properties of Banach spaces, as well as specialists in nonlinear operator theory. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1965 606 $aOperator theory 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aFunctional analysis 606 $aCalculus of variations 606 $aIntegral equations 606 $aNumerical analysis 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aOperator theory. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aFunctional analysis. 615 0$aCalculus of variations. 615 0$aIntegral equations. 615 0$aNumerical analysis. 615 14$aOperator Theory. 615 24$aAnalysis. 615 24$aFunctional Analysis. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aIntegral Equations. 615 24$aNumerical Analysis. 676 $a515.732 686 $aMAT 462f$2stub 686 $aMAT 476f$2stub 686 $aMAT 652f$2stub 686 $aSI 850$2rvk 700 $aChidume$b Charles$4aut$4http://id.loc.gov/vocabulary/relators/aut$0606379 906 $aBOOK 912 $a996466526203316 996 $aGeometric properties of banach spaces and nonlinear iterations$91120451 997 $aUNISA