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1.

図書

東工大
目次DB

図書
東工大
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editors, Wataru Takahashi, Tamaki Tanaka
出版情報: Singapore : World Scientific, c1999  xi, 388 p. ; 23 cm
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Introduction
Invited Papers
   Second Derivatives in Convex Analysis R. Tyrrell Rockafellar 3
   Dunford-Pettis-Types Theorem and Convergences in Set-Valued Integration Charles Castaing, Mohammed Saadoune 8
   Second-Order Analysis of the Moreau-Yosida Regularization Liqun Qi 16
   Existence of Equilibria for G-Monotone Mappings Werner Oettli, D. Schlaeger 26
   Programming Problems Involving Generalized Convex Set Functions Hang-Chin Lai 34
   A Noncooperative Equilibrium for n-Person Game with Fractional Loss Function Yutaka Kimura, Yoichi Sawasaki, Kensuke Tanaka 44
   Reframing Multicriteria Games for Win-Win Solution Po Lung Yu, J.M. Li 52
   Time Consistency of Cooperative Solutions in Dynamic Games Leon A. Petrosjan 61
   A Survey on Some Recent Results in Nonlinear Functional Analysis Biagio Ricceri 65
   Fixed Point Properties for Semigroups of Nonexpansive Mappings Anthony T.-M. Lau 72
   Remarks on a Fixed Point of Ben-El-Mechaiekh Sehie Park 79
   Fixed Point Theorems, Convergence Theorems and Their Applications Wataru Takahashi 87
Contributed Papers
   The Homeomorphism Problem of Compact Nonlinear Mappings Shigeo Akashi 97
   A Weak Convergence Theorem for Nonexpansive Semigroups by the Mannn Iteration Process in Banach Spaces Sachiko Atsushiba, Wataru Takahashi 102
   The Core and the Dominance Core in Multichoice Multistage Games with Coalitions in Matrix Form Dmitri A. Ayoshin, Tamaki Tanaka 110
   Fixed Points for Set-Valued Maps: A Topological Perspective Hichem Ben-El-Mechaiekh 118
   On the Random Product of Orthogonal Projections in Hilbert Space Jean-Bernard Baillon, Ronald E. Bruck 126
   Inhomogeneous Iterates and Nonlinear Weak Ergodic Theorems Yong-Zhuo Chen 134
   Ultimately Compact Operators in Hyperconvex Metric Spaces Rafael Espinola, Genaro Lopez 142
   Rotative Mappings in Metric Fixed Point Theory Kazimierz Goebel, Malgorzata Koter-Morgowska 150
   A Solution for a Two-Person Zero-Sum Game with a Concave Payoff Function Ryusuke Hohzaki, Koji Iida 157
   The Leray-Schauder Alternative for Nonexpansive Maps from the Ball Characterize Hilbert Space Michael Ireland, William A. Kirk, Brailey Sims 167
   Euler Partition Rule Seiichi Iwamoto 173
   On Semicontinuity of Set-Valued Maps and Marginal Functions Yutaka Kimura, Kensuke Tanaka, Tamaki Tanaka 181
   Euclidean Isometries of Julia Sets of Polynomials Masashi Kisaka 189
   A Note on Fixed Point Properties in Abstract Convex Spaces Hidetoshi Komiya 196
   Generalized Supremum in Partially Ordered Linear Space Naoto Komuro, Shozo Koshi 199
   Controlled Markov Set-Chains with Set-Valued Rewards Masami Kurano, Jun-ichi Nakagami, Masayuki Horiguchi 205
   On Pseudo-Fourier Transforms Yukio Kuribayashi 213
   Some Duality Theorems of Set-Valued Optimization with Natural Criteria Daishi Kuroiwa 221
   The Characterization of Generalized KKM Mappings with Finitely Open Values in Topological Vector Spaces Byung-Soo Lee, Yeol Je Cho, George Xian-Zhi Yuan 229
   On Generalized Loose Saddle Point Theorems for Set-Valued Maps Lai-Jiu Lin 237
   A Duality Theorem in Multiobjective Routing Problems with Associative Path Costs Yukihiro Maruyama 245
   A Note on the Nucleolus of Assignment Games Tomomi Matsui 253
   Complexity Results for Calculating Power Indices of Weighted Majority Games Yasuko Matsui 261
   Local Connectedness of Julia Sets for Transcendental Entire Functions Shunsuke Morosawa 266
   Parabolic Components for a Family of Cubic Polynomials Shizuo Nakane 274
   General Inverse Theorems for the Best Approximation in Banach Spaces Toshihiko Nishishiraho 281
   Bifurcations and Hyperbolic Components Kiyoko Nishizawa, Masayo Fujimura 289
   Gale's Feasibility Theorem and Max-Flow Problems in a Continuous Network Ryohei Nozawa 297
   Optimality in Multi-Person Stopping Problem with General Rewards Yoshio Ohtsubo 305
   A Refinement of the Concept of Equilibrium in Multiple Objective Games Justo Puerto, Francisco R. Fernandez 313
   Existence Criteria for Fuzzy Optimization Problems Seiji Saito, Hiroaki Ishii 321
   The Extended Semidefinite Linear Complementarity Problem: A Reformulation Approach Masahiro Shibata, Nobuo Yamashita, Masao Fukushima 326
   On the Level Set Method in Minimax Theory L.L. Stacho 333
   On Weak Convergence to Fixed Points of Nonexpansive Mappings in Banach Spaces Tomonari Suzuki, Wataru Takahashi 341
   A Necessary and Sufficient Condition for Equality in the Marcus Inequality Sin-Ei Takahasi, Ritsuo Nakamoto 348
   Supremum of a Set in the Multi-Dimensional Extended Real Space Tetsuzo Tanino 352
   Solution Concepts in Bargaining Masayo Tsurumi, Tetsuzo Tanino, Masahiro Inuiguchi 360
   An Inner Approximation Method for Optimization over the Weakly Efficient Set Syuuji Yamada, Tetsuzo Tanino, Masahiro Inuiguchi 368
   Relationships between Efficient Set and ε-Efficient Set Kazunori Yokoyama 376
Introduction
Invited Papers
   Second Derivatives in Convex Analysis R. Tyrrell Rockafellar 3
2.

図書

図書
H. Umegaki & W. Takahashi, (eds.)
出版情報: [Tokyo : Symposium on Applied Functional Analysis], 1991  118 p. ; 26 cm
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3.

図書

東工大
目次DB

図書
東工大
目次DB
高橋渉著
出版情報: 横浜 : 横浜図書, 1999.3  iv, 232p ; 21cm
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第1章 基本概念 1
   1.1 数列の極限 1
   1.2 級数 9
   1.3 関数の極限 16
第2章 微分 22
   2.1 微分係数と導関数 22
   2.2 逆関数の導関数 29
   2.3 平均値の定理 35
   2.4 高階の導関数 42
   2.5 凸関数と近似値 49
第3章 積分 56
   3.1 定積分の定義 56
   3.2 定積分の基本的性質 63
   3.3 基本関数の不定積分 70
   3.4 やや複雑な不定積分 76
   3.5 広義積分 83
第4章 2変数関数の微分 90
   4.1 2変数関数と偏微分 90
   4.2 全微分と合成関数の微分法 97
   4.3 2変数のテイラーの定理 104
   4.4 陰関数定理 111
第5章 2変数関数の積分 117
   5.1 重積分の定義とその計算 117
   5.2 重積分の性質と変数変換 124
   5.3 広義重積分 131
第6章 関数の級数 138
   6.1 べき級数 138
   6.2 一様収束性 145
   6.3 一様収束性と微分積分 151
第7章 微分方程式 158
   7.1 1階微分方程式-変数分離形,同次形 158
   7.2 1階微分方程式-線形,完全形 164
第8章 特論 170
   8.1 上極限・下極限 170
   8.2 コーシーの判定条件と収束定理 178
解答の略解 185
参考文献 228
索引 229
第1章 基本概念 1
   1.1 数列の極限 1
   1.2 級数 9
4.

図書

図書
高橋渉著
出版情報: 横浜 : 横浜図書, 2001.10  iv, 181p ; 22cm
シリーズ名: 数理解析入門シリーズ ; 1
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5.

図書

東工大
目次DB

図書
東工大
目次DB
Wataru Takahashi
出版情報: Yokohama : Yokohama Publishers, c2000  iv, 276 p. ; 23 cm
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Introduction
Invited Papers
   Second Derivatives in Convex Analysis R. Tyrrell Rockafellar 3
   Dunford-Pettis-Types Theorem and Convergences in Set-Valued Integration Charles Castaing, Mohammed Saadoune 8
   Second-Order Analysis of the Moreau-Yosida Regularization Liqun Qi 16
   Existence of Equilibria for G-Monotone Mappings Werner Oettli, D. Schlaeger 26
   Programming Problems Involving Generalized Convex Set Functions Hang-Chin Lai 34
   A Noncooperative Equilibrium for n-Person Game with Fractional Loss Function Yutaka Kimura, Yoichi Sawasaki, Kensuke Tanaka 44
   Reframing Multicriteria Games for Win-Win Solution Po Lung Yu, J.M. Li 52
   Time Consistency of Cooperative Solutions in Dynamic Games Leon A. Petrosjan 61
   A Survey on Some Recent Results in Nonlinear Functional Analysis Biagio Ricceri 65
   Fixed Point Properties for Semigroups of Nanoexpansive Mappings Anthony T.-M. Lau 72
   Remarks on a Fixed Point Problem of Ben-El-Mechaiekh Sehie Park 79
   Fixed Point Theorems, Convergence Theorems and Their Applications Wataru Takahashi 87
Contributed Papers
   The Homeomorphism Problem of Compact Nonlinear Mappings Shigeo Akashi 97
   A Weak Convergence Theorem for Nonexpansive Semigroups by the Mann Iteration Process in Banach Spaces Sachiko Atsushiba, Wataru Takahashi 102
   The Core and the Dominance Core in Multichoice Multistage Games with Coalitions in Matrix Form Dmitri A. Ayoshin, Tamaki Tanaka 110
   Fixed Points for Set-Valued Maps: A Topological Perspective Hichem Ben-El-Mechaiekh 118
   On the Random Product of Orthogonal Projection in Hilbert Space Jean-Bernard Baillon, Ronald E. Bruck 126
   Inhomogeneous Iterates and Nonlinear Weak Ergodic Theorems Yong-Zhuo Chen 134
   Ultimately Compact Operators in Hyperconvex Metric Spaces Rafael Espinola, Genaro Lopez 142
   Rotative Mappings in Metric Fixed Point Theory Kazimierz Goebel, Malgorzata Koter-Morgowska 150
   A Solution for a Two-Person Zero-Sum Game with a Concave Payoff Function Ryusuke Hohzaki, Koji Iida 157
   The Leray-Schauder Alternative for Nonexpansive Maps from the Ball Characterize Hilbert Space Michael Ireland, William A. Kirk, Brailey Sims 167
   Euler Partition Rule Seiichi Iwamoto 173
   On Semicontinuity of Set-Valued Maps and Marginal Functions Yutaka Kimura, Kensuke Tanaka, Tamaki Tanaka 181
   Euclidean Isometries of Julia Sets of Polynomials Masashi Kisaka 189
   A Note on Fixed Point Properties in Abstract Convex Spaces Hidetoshi Komiya 196
   Generalized Supremum in Partially Ordered Linear Space Naoto Komuro, Shozo Koshi 199
   Controlled Markov Set-Chains with Set-Valued Rewards Masami Kurano, Jun-ichi Nakagami, Masayuki Horiguchi 205
   On Pseudo-Fourier Transforms Yukio Kuribayashi 213
   Some Duality Theorems of Set-Valued Optimization with Natural Criteria Daishi Kuroiwa 221
   The Characterization of Generalized KKM Mappings with Finitely Open Values in Topological Vector Spaces Byung-Soo Lee, Yeol Je Cho, George Xian-Zhi Yuan 229
   On Generalized Loose Saddle Point Theorems for Set-Valued Maps Lai-Jiu Lin 237
   A Duality Theorem in Multiobjective Routing Problems with Associative Path Costs Yukihiro Maruyama 245
   A Note on the Nucleolus of Assignment Games Tomomi Matsui 253
   Complexity Results for Calculating Power Indices of Weighted Majority Games Yasuko Matsui 261
   Local Connectedness of Julia Sets for Transcendental Entire Functions Shunsuke Morosawa 266
   Parabolic Components for a Family of Cubic Polynomials Shizuo Nakane 274
   General Inverse Theorems for the Best Approximation in Banach Spaces Toshihiko Nishishiraho 281
   Bifurcations and Hyperbolic Components Kiyoko Nishizawa, Masayo Fujimura 289
   Gale's Feasibility Theorem and Max-Flow Problems in a Continuous Network Ryohei Nozawa 297
   Optimality in Multi-Person Stopping Problem with General Rewards Yoshio Ohtsubo 305
   A Refinement of the Concept of Equilibrium in Multiple Objective Games Justo Puerto, Francisco R. Fernandez 313
   Existence Criteria for Fuzzy Optimization Problems Seiji Saito, Hiroaki Ishii 321
   The Extended Semidefinite Linear Complementarity Problem: A Reformulation Approach Masahiro Shibata, Nobuo Yamashita, Masao Fukushima 326
   On the Level Set Method in Minimax Theory L.L. Stacho 333
   On Weak Convergence to Fixed Points of Nanoexpansive Mappings in Banach Spaces Tomonari Suzuki, Wataru Takahashi 341
   A Necessary and Sufficient Condition for Equality in the Marcus Inequality Sin-Ei Takahasi, Ritsuo Nakamoto 348
   Supremum of a Set in the Multi-Dimensional Extended Real Space Tetsuzo Tanino 352
   Solution Concepts in Bargaining Masayo Tsurumi, Tetsuzo Tanino, Masahiro Inuiguchi 360
   An Inner Approximation Method for Optimization over the Weakly Efficient Set Syuuji Yamada, Tetsuzo Tanino, Masahiro Inuiguchi 368
   Relationships between Efficient Set and ε-Efficient Set Kazunori Yokoyama 376
Introduction
Invited Papers
   Second Derivatives in Convex Analysis R. Tyrrell Rockafellar 3
6.

図書

東工大
目次DB

図書
東工大
目次DB
青木利夫, 高橋渉共著
出版情報: 東京 : 培風館, 1979.9  iii, 188p ; 22cm
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第1章 論理
   §1 命題 1
   §2 推論 7
   §3 命題関数 12
第2章 集合
   §1 集合と演算 17
   §2 写像・集合族 22
   §3 集合族の演算・直積 26
   §4 関係・順序 30
   §5 無限集合 36
第3章 距離空間
   §1 距離空間の定義 41
   §2 開集合 46
   §3 閉集合 51
   §4 極限と近傍 55
   §5 写像の連続 60
   §6 完備性 65
第4章 位相空間
   §1 位相空間の定義 70
   §2 基礎概念 75
   §3 連続写像 80
   §4 部分空間と直積空間 85
   §5 可算公理・連結性 90
   §6 分離条件 95
   §7 コンパクト性 100
   §8 コンパクト性(続き) 104
第5章 Banach空間
   §1 ノルム空間 108
   §2 Banach空間の定義 113
   §3 連続線形作用素 117
第6章 Hilbert空間
   §1 Hilbert空間の定義 121
   §2 関数空間・直交性 126
   §3 完全正規直交系 131
   §4 直交分解・線形汎関数 136
第7章 特論
   §1 濃度の比較 140
   §2 Moore-Smithの収束 145
   §3 距離づけの問題 149
   §4 局所コンパクト空間 153
   §5 Zornの補題とTibonovの定理 156
   §6 Hahn-Banachの定理 161
   問題の略解 165
   索引 183
   記号索引 188
第1章 論理
   §1 命題 1
   §2 推論 7
7.

図書

東工大
目次DB

図書
東工大
目次DB
青木利夫, 高橋渉, 平野載倫共著
出版情報: 東京 : 培風館, 1985.11  iii, 200p ; 22cm
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第1章 論理
   1 命題 1
   2 推論 6
   3 命題関数 12
第2章 集合
   1 集合と演算 17
   2 写像・集合族 23
   3 集合族の演算・直積 28
   4 関係・順序 33
   5 無限集合 38
第3章 距離空間
   1 距離空間の定義 43
   2 開集合 49
   3 閉集合 54
   4 極限と近傍 59
   5 写像の連続 65
   6 完備性 71
第4章 位相空間
   1 位相空間の定義 76
   2 基礎概念 81
   3 連続写像 87
   4 部分空間と直積空間 93
   5 可算公理・連結性 99
   6 分離条件 105
   7 コンパクト性 111
第5章 Banach空間
   1 ノルム空間 117
   2 Banach空間 123
   3 連続線形作用素 129
第6章 Hilbert空間
   1 Hilbert空間の定義 136
   2 関数空間・直交性 142
   3 空全正規直交系 148
   4 直交分解・線形汎関数 154
第7章 特論
   1 濃度の比較 160
   2 Moore-Smithの収束 166
   3 距離づけの問題 172
   4 局所コンパクト空間 178
   5 Zornの補題とTihonovの定理 183
   5 Hahn-Banachの定理 189
   索引 195
   記号索引 200
第1章 論理
   1 命題 1
   2 推論 6
8.

図書

東工大
目次DB

図書
東工大
目次DB
高橋渉著
出版情報: 横浜 : 横浜図書, 2000.7  iv, 278p ; 22cm
シリーズ名: 数理解析シリーズ ; 2
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1.準備 1
   1.1 距離空間と位相空間 1
   1.2 Banach 空間と Hibbert 空間 13
   1.3 線形位相空間 28
2.下半連続関数と凸関数 36
   2.1 区間上での凸関数 36
   2.2 下半連続関数と凸関数の基本的性質 44
   2.3 完備距離空間での下半連続関数 53
   2.4 Banach 空間上での凸関数 62
   2.5 Minimax 定理 70
   2.6 Hahn-Banach の定理の拡張定理 78
3. 増大作用素と単調作用素 86
   3.1 Banach 空間のノルムの凸性 86
   3.2 Banach 空間の双対写像 94
   3.3 Banach 空間のノエムの微分可能性 103
   3.4 増大作用素 110
   3.5 単調作用素 120
4. 方向微分と劣微分 128
   4.1 方向微分と劣微分の定義と例 128
   4.2 共役関数と劣微分 138
   4.3 ε-劣微分と劣微分 146
   4.4 Rockafellar の定理 154
   4.5 劣微分と極大単調作用素 163
5. 不動点近似法 170
   5.1 Hilbert 空間での不動点近似法 170
   5.2 増大作用素のリゾンベルトの収束定理 177
   5.3 一様凸 Banach 空間での非拡大写像 185
   5.4 Banach 空間での不動点近似法 193
6. 応用 200
   6.1 制約可能性問題 200
   6.2 近接点法 208
   6.3 Kuhn-Tucker の定理 217
   6.4 双対問題 224
問題の略解 232
参考文献 260
索引 272
記号一覧 277
1.準備 1
   1.1 距離空間と位相空間 1
   1.2 Banach 空間と Hibbert 空間 13
9.

図書

東工大
目次DB

図書
東工大
目次DB
editors, Toshiaki Murohushi, Wataru Takahashi, Makoto Tsukada
出版情報: Yokohama : Yokohama Publishers, c2007  iv, 301 p. ; 23 cm
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Preface i
Masamu Nagisa,Makoto Ueda,and Shuhei Wada
Commutativity induced from some operator identities 1
Akira Igarashi
On non-commutative general topology 7
Masanori Ohya
Mathematical foundation of quantum teleportation 21
Masayuki Miyashita and Noboru Watanabe
On a model of quantum teleportation using entangled
state generated by squeezed state and beam splitter 45
Jun Ichi Fujii
Reduced linear codes from cyclic ones 55
Shoichi Nishimura
A spectral method calculating the stationary vector
for a BMAP/G/1queue 63
Toshiaki Murofushi, Yoshinari Sawata, and Katsushige Fujimoto
Additive decompositions of submodular set functions
and their generalizations 73
Aoi Honda and Yoshiaki Okazaki
Generalization of Shannon entropy of capacities
on set systems 89
Makoto Tsukada, Hiroki Suyari, and Masahiko Kato
On the probability distribution maximizing generalized entropies 99
Kenjiro Yanagi, Shigeru Furuichi and Ken Kuriyama
On generalized skew information 113
Yatsuka Nakamura and Yasunari Shidama
Mizar mathematical library and funtional analysis 125
Masatoshi Fujii, Eizaburo Kamei and Ritsuo Nakamoto
An extension of Ando-Hiai theorem and its application 137
Yasuo Narukawa
Fundamental theorems in functional analyasis for
non-additive measure theory 145
Sachiko Atsushiba
Weak convergence theorems for a countable family
of nonexpansive mappings in Banach spaces satisfying
Opial's condition 153
Yoshiyuki Sekiguchi
Regularity in optimization problems and its quantitative analysis 169
Masahiko Kato
Company supported framelets and the Ruelle operators 177
Yasunori Kimura
On a strong convergence theorem of resolvents
for maximal monotone operators in a Banach space 193
Takeshi Miura, Hiroyuki Takagi, and Sin-ei Takahasi
A generalization of Wang's inequality 203
Yoshinori Uesaka
How to extract rough sketches from a form? 211
Wataru Takahashi
Approximating solutions of accretive operators by
viscosity approximation methods in Banach spaces 225
Jun Tomiyama
On the structure of the spaces of matrix monotone
functions and of matrix convex functions 245
Yuichiro Kakihara
Integration with respect to Hilbert-Schmidt class
operator valued measures 263
Jun Kawabe
The countably subnormed Riesz space with applications
to nonadditive measure theory 279
Naofumi Muraki
Different Gaussianizations of probability measure
given by(入,q)-Fock space 293
Preface i
Masamu Nagisa,Makoto Ueda,and Shuhei Wada
Commutativity induced from some operator identities 1
10.

図書

東工大
目次DB

図書
東工大
目次DB
高橋渉著
出版情報: 東京 : 近代科学社, 1988.5  iv, 241p ; 22cm
シリーズ名: 現代数学ゼミナール ; 7
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1.非線形関数解析学を学ぶための準備 1
   1.1 位相空間 1
   1.2 Banach空間,Hilbert空間 9
   1.3 下半連続関数と凸関数 17
   1.4 完備距離空間における存在定理 24
   1.5 Banach limit と invariant mcan 31
2.Hilbert空間における不動点理論 38
   2.1 Hilbert空間での不動点定理 38
   2.2 不動点への収束定理 45
   2.3 Rayの定理 51
   2.4 非可換半群の不動点定理 58
   2.5 一般化された非線形エルゴード定理 64
   2.6 種々の非線形エルゴード定理 70
   2.7 Ergodic retraction 76
3.Banach空間の幾何学 82
   3.1 Banach空間の凸性 82
   3.2 双対写像とノルムの微分可能性 88
   3.3 双対写像とノルムの微分可能性(2) 95
   3.4 nonexpansive写像の不動点定理 102
   3.5 写像族に対する不動点定理 109
   3.6 増大作用素 116
4.Banach空間における収束定理 123
   4.1 Resolventの収束 123
   4.2 Resolventの収束(2) 129
   4.3 Banach空間での非線形エルゴード定理 135
   4.4 線形作用素に対するエルゴード定理 143
5.線形位相空間における不動点理論 150
   5.1 Fan-Browderの不動点定理 150
   5.2 拡張された不動点定理 155
   5.3 minimax定理 161
   5.4 Mazur-Orliczの定理 168
   5.5 分離定理,最短距離定理 174
6.不動点理論の応用 180
   6.1 変分不等式と相補性問題 180
   6.2 ゲームのcore 186
   6.3 線形作用素への応用 192
   6.4 線形不等式と最小ノルム問題 199
参考文献 207
問題の略解 219
和文索引 236
欧文索引 238
記号一覧 240
1.非線形関数解析学を学ぶための準備 1
   1.1 位相空間 1
   1.2 Banach空間,Hilbert空間 9
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