The Resource From HahnBanach to monotonicity, Stephen Simons
From HahnBanach to monotonicity, Stephen Simons
Resource Information
The item From HahnBanach to monotonicity, Stephen Simons represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item From HahnBanach to monotonicity, Stephen Simons represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique"for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the HahnBanach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space
 Language
 eng
 Edition
 2nd, expanded ed.
 Extent
 1 online resource (xiv, 244 pages)
 Note
 "These notes are somewhere between a sequel to and a new edition of [Minimax and monotonicity, c1998]"Page viii
 Contents

 36. Subclasses of the maximally monotone multifunctions
 37. First application of Theorem 35.8: type (D) implies type (FP)
 38. TCLB(E), TCLBN(B) and type (ED)
 39. Second application of Theorem 35.8: type (ED) implies type (FPV)
 40. Second applications of Theorem 35.8: type (ED) implies strong
 41. Strong maximality and coercivity
 42. Type (ED) implies type (ANA) and type (BR)
 43. The closure of the range
 44. The sum problem and the closure of the domain
 45. The biconjugate of a maximum TCLB(E**)
 46. Maximally monotone multifunctions with convex graph
 47. Possibly discontinuous positive linear operators
 48. Subtler properties of subdifferentials
 49. Saddle functions and type (ED)
 VII. The sum problem for general Banach spaces
 50. Introductory comments
 51. Voisei's theorem
 52. Sums with normality maps
 53. A theorem of VeronaVerona
 Isbn
 9781402069185
 Label
 From HahnBanach to monotonicity
 Title
 From HahnBanach to monotonicity
 Statement of responsibility
 Stephen Simons
 Subject

 Banach spaces
 Banach spaces
 Banach spaces
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Maxima and minima
 Maxima and minima
 Maxima and minima
 Maxima and minima
 Monotone operators
 Monotone operators
 Monotone operators
 Monotone operators
 Monotonic functions
 Monotonic functions
 Monotonic functions
 Monotonic functions
 Banach spaces
 Language
 eng
 Summary
 In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a "big convexification" of the graph of the multifunction and the "minimax technique"for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the HahnBanach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Simons, S
 Dewey number
 515.7248
 Illustrations
 illustrations
 Index
 index present
 LC call number

 QA329.8
 QA3
 LC item number

 .S58 2008eb
 .L28 no. 1693 2008
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Simons, S
 Series statement
 Lecture notes in mathematics,
 Series volume
 1693
 http://library.link/vocab/subjectName

 Monotone operators
 Monotonic functions
 Maxima and minima
 Duality theory (Mathematics)
 Banach spaces
 Maxima and minima
 Duality theory (Mathematics)
 Banach spaces
 Monotone operators
 Monotonic functions
 Banach spaces
 Duality theory (Mathematics)
 Maxima and minima
 Monotone operators
 Monotonic functions
 Label
 From HahnBanach to monotonicity, Stephen Simons
 Note
 "These notes are somewhere between a sequel to and a new edition of [Minimax and monotonicity, c1998]"Page viii
 Bibliography note
 Includes bibliographical references (pages 233238) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 36. Subclasses of the maximally monotone multifunctions  37. First application of Theorem 35.8: type (D) implies type (FP)  38. TCLB(E), TCLBN(B) and type (ED)  39. Second application of Theorem 35.8: type (ED) implies type (FPV)  40. Second applications of Theorem 35.8: type (ED) implies strong  41. Strong maximality and coercivity  42. Type (ED) implies type (ANA) and type (BR)  43. The closure of the range  44. The sum problem and the closure of the domain  45. The biconjugate of a maximum TCLB(E**)  46. Maximally monotone multifunctions with convex graph  47. Possibly discontinuous positive linear operators  48. Subtler properties of subdifferentials  49. Saddle functions and type (ED)  VII. The sum problem for general Banach spaces  50. Introductory comments  51. Voisei's theorem  52. Sums with normality maps  53. A theorem of VeronaVerona
 Control code
 233972679
 Dimensions
 unknown
 Edition
 2nd, expanded ed.
 Extent
 1 online resource (xiv, 244 pages)
 Form of item
 online
 Isbn
 9781402069185
 Lccn
 2007942159
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781402069185
 Specific material designation
 remote
 System control number
 (OCoLC)233972679
 Label
 From HahnBanach to monotonicity, Stephen Simons
 Note
 "These notes are somewhere between a sequel to and a new edition of [Minimax and monotonicity, c1998]"Page viii
 Bibliography note
 Includes bibliographical references (pages 233238) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 36. Subclasses of the maximally monotone multifunctions  37. First application of Theorem 35.8: type (D) implies type (FP)  38. TCLB(E), TCLBN(B) and type (ED)  39. Second application of Theorem 35.8: type (ED) implies type (FPV)  40. Second applications of Theorem 35.8: type (ED) implies strong  41. Strong maximality and coercivity  42. Type (ED) implies type (ANA) and type (BR)  43. The closure of the range  44. The sum problem and the closure of the domain  45. The biconjugate of a maximum TCLB(E**)  46. Maximally monotone multifunctions with convex graph  47. Possibly discontinuous positive linear operators  48. Subtler properties of subdifferentials  49. Saddle functions and type (ED)  VII. The sum problem for general Banach spaces  50. Introductory comments  51. Voisei's theorem  52. Sums with normality maps  53. A theorem of VeronaVerona
 Control code
 233972679
 Dimensions
 unknown
 Edition
 2nd, expanded ed.
 Extent
 1 online resource (xiv, 244 pages)
 Form of item
 online
 Isbn
 9781402069185
 Lccn
 2007942159
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations.
 http://library.link/vocab/ext/overdrive/overdriveId
 9781402069185
 Specific material designation
 remote
 System control number
 (OCoLC)233972679
Subject
 Banach spaces
 Banach spaces
 Banach spaces
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Duality theory (Mathematics)
 Maxima and minima
 Maxima and minima
 Maxima and minima
 Maxima and minima
 Monotone operators
 Monotone operators
 Monotone operators
 Monotone operators
 Monotonic functions
 Monotonic functions
 Monotonic functions
 Monotonic functions
 Banach spaces
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