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Эта публикация цитируется в 104 научных статьях (всего в 104 статьях)
Математические обзоры
Идемпотентный функциональный анализ. Алгебраический подход
Г. Л. Литвиновa, В. П. Масловb, Г. Б. Шпизa a Международный центр "Софус Ли"
b Московский государственный университет им. М. В. Ломоносова, физический факультет
Аннотация:
Статья посвящена идемпотентному функциональному анализу, который является “абстрактной” версией идемпотентного анализа, разработанного В. П. Масловым и его
сотрудниками. Дан обзор основных идей идемпотентного анализа. Обсуждается соответствие между концепциями и теоремами традиционного функционального анализа и его идемпотентной версии в духе принципа соответствия Н. Бора в квантовой теории. Представлен алгебраический подход к идемпотентному функциональному анализу. Основные понятия и результаты сформулированы в алгебраических терминах; при
этом существенно, что операция идемпотентного сложения может быть определена для бесконечного множества слагаемых. Исследованы идемпотентные аналоги основных
принципов линейного анализа и результатов об общем виде линейного функционала и о скалярных произведениях на идемпотентных пространствах.
Библиография: 81 название.
DOI:
https://doi.org/10.4213/mzm539
Полный текст:
PDF файл (428 kB)
Список литературы:
PDF файл
HTML файл
Англоязычная версия:
Mathematical Notes, 2001, 69:5, 696–729
Реферативные базы данных:
УДК:
519 Поступило: 17.05.2000
Образец цитирования:
Г. Л. Литвинов, В. П. Маслов, Г. Б. Шпиз, “Идемпотентный функциональный анализ. Алгебраический подход”, Матем. заметки, 69:5 (2001), 758–797; Math. Notes, 69:5 (2001), 696–729
Цитирование в формате AMSBIB
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\jour Матем. заметки
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Russian articles,
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Эта публикация цитируется в следующих статьяx:
-
Litvinov, GL, “Nuclear semimodules and kernel theorems in idempotent analysis: An algebraic approach”, Doklady Mathematics, 66:2 (2002), 197
-
Litvinov G., Maslov V., Shpiz G., “Idempotent (Asymptotic) Mathematics and the Representation Theory”, Asymptotic Combinatorics with Applications to Mathematical Physics, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 77, eds. Malyshev V., Vershik A., Springer, 2002, 267–278
-
С. Н. Сергеев, “Алгоритмическая сложность одной задачи
идемпотентно выпуклой геометрии”, Матем. заметки, 74:6 (2003), 896–901
; S. N. Sergeev, “Algorithmic Complexity of a Problem of Idempotent Convex Geometry”, Math. Notes, 74:6 (2003), 848–852 -
McEneaney, WM, “Max-plus eigenvector methods for nonlinear H-infinity problems: Error analysis”, SIAM Journal on Control and Optimization, 43:2 (2004), 379
-
Katsov, Y, “On flat semimodules over semirings”, Algebra Universalis, 51:2–3 (2004), 287
-
Gaubert, S, “Rational semimodules over the max-plus semiring and geometric approach to discrete event systems”, Kybernetika, 40:2 (2004), 153
-
Cohen, G, “Duality and separation theorems in idempotent semimodules”, Linear Algebra and Its Applications, 379 (2004), 395
-
Kim, KH, “Inclines and incline matrices: a survey”, Linear Algebra and Its Applications, 379 (2004), 457
-
McEneaney W., “Combining Legendre/Fenchel Transformed Operators on Max-Plus Spaces for Nonlinear Control Solution”, 2004 43rd IEEE Conference on Decision and Control (CDC), Vols 1-5, IEEE Conference on Decision and Control - Proceedings, IEEE, 2004, 1152–1157
-
Г. Л. Литвинов, “Деквантование Маслова, идемпотентная и тропическая математика: краткое введение”, Теория представлений, динамические системы, комбинаторные и алгоритмические методы. XIII, Зап. научн. сем. ПОМИ, 326, ПОМИ, СПб., 2005, 145–182
; G. L. Litvinov, “The Maslov dequantization, idempotent and tropical mathematics: a brief introduction”, J. Math. Sci. (N. Y.), 140:3 (2007), 426–444 -
McEneaney W.M., “Curse-of-Dimensionality Free Method for Bellman PDEs with Hamiltonian Written as Maximum of Quadratic Forms”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 42–47
-
Akian M., Gaubert S., Lakhoua A., “The Max-Plus Finite Element Method for Optimal Control Problems: Further Approximation Results”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 4505–4510
-
Akian M., Gaubert S., Kolokoltsov V., “Solutions of Max-Plus Linear Equations and Large Deviations”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, IEEE Conference on Decision and Control - Proceedings, IEEE, 2005, 7787–7792
-
Litvinov G., “The Maslov Dequantization, Idempotent and Tropical Mathematics: a Very Brief Introduction”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, 377, ed. Litvinov G. Maslov V., Amer Mathematical Soc, 2005, 1–17
-
Akian M., Gaubert S., Walsh C., “Discrete Max-Plus Spectral Theory”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 53–77
-
Cohen G., Gaubert S., Quadrat J., Singer I., “Max-Plus Convex Sets and Functions”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics Series, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 105–129
-
Litvinov G., Shpiz G., “The Dequantization Transform and Generalized Newton Polytopes”, Idempotent Mathematics and Mathematical Physics, Contemporary Mathematics Series, 377, eds. Litvinov G., Maslov V., Amer Mathematical Soc, 2005, 181–186
-
Г. Л. Литвинов, Г. Б. Шпиз, “Теоремы о ядре и ядерность в идемпотентной математике. Алгебраический подход”, Теория представлений, динамические системы, комбинаторные и алгоритмические методы. XIV, Зап. научн. сем. ПОМИ, 331, ПОМИ, СПб., 2006, 60–83
; G. L. Litvinov, G. B. Shpiz, “Kernel theorems and nuclearity in idempotent mathematics. An algebraic approach”, J. Math. Sci. (N. Y.), 141:4 (2007), 1417–1428 -
Gaubert, S, “Max-plus convex geometry”, Relations and Kleene Algebra in Computer Science, Proceedings, 4136 (2006), 192
-
McEneaney W.M., “Curse-of-Dimensionality Free Method for Bellman PDEs with Semiconvex Hamiltonians”, Proceedings of the 45th IEEE Conference on Decision and Control, Vols 1-14, IEEE Conference on Decision and Control, IEEE, 2006, 967–972
-
С. Гобер, С. Н. Сергеев, “Циклические проекторы и теоремы отделимости в идемпотентных полумодулях”, Фундамент. и прикл. матем., 13:4 (2007), 31–52
; S. Gaubert, S. N. Sergeev, “Cyclic projectors and separation theorems in idempotent convex geometry”, J. Math. Sci., 155:6 (2008), 815–829 -
Г. Б. Шпиз, “Теорема о существовании собственного вектора в идемпотентном анализе”, Матем. заметки, 82:3 (2007), 459–468
; G. B. Shpiz, “An Eigenvector Existence Theorem in Idempotent Analysis”, Math. Notes, 82:3 (2007), 410–417 -
McEneaney W. M., “A curse-of-dimensionality-free numerical method for solution of certain HJB PDEs”, SIAM J. Control Optim., 46:4 (2007), 1239–1276
-
McEneaney, WM, “Max-plus summation of Fenchel-transformed semigroups for solution of nonlinear Bellman equations”, Systems & Control Letters, 56:4 (2007), 255
-
Sergeev, S, “Max-plus definite matrix closures and their eigenspaces”, Linear Algebra and Its Applications, 421:2–3 (2007), 182
-
Gaubert, S, “The Minkowski theorem for max-plus convex sets”, Linear Algebra and Its Applications, 421:2–3 (2007), 356
-
Nitica, V, “Max-plus convex sets and max-plus semispaces. I”, Optimization, 56:1–2 (2007), 171
-
McEneaney W.M., “Using Semiconvex Duality and Max-Plus Analysis to Obtain a New Fundamental Solution for the Differential Riccati Equation”, Proceedings of the 46th IEEE Conference on Decision and Control, Vols 1-14, IEEE Conference on Decision and Control - Proceedings, IEEE, 2007, 3032–3037
-
Л. Е. Базилевич, “Гиперпространство max-плюс выпуклых компактных множеств”, Матем. заметки, 84:5 (2008), 658–666
; L. E. Bazilevich, “Hyperspace of Max-Plus Convex Compact Sets”, Math. Notes, 84:5 (2008), 615–622 -
Briec, W, “Halfspaces and Hahn-Banach like properties in B-convexity and Max-Plus convexity”, Pacific Journal of Optimization, 4:2 (2008), 293
-
Hubal, O, “Idempotent probability measures on ultrametric spaces”, Journal of Mathematical Analysis and Applications, 343:2 (2008), 1052
-
McEneaney, WM, “A new fundamental solution for differential Riccati equations arising in control”, Automatica, 44:4 (2008), 920
-
Akian, M, “The max-plus finite element method for solving deterministic optimal control problems: Basic properties and convergence analysis”, SIAM Journal on Control and Optimization, 47:2 (2008), 817
-
Briec, W, “Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and B-convexity”, Journal of Mathematical Analysis and Applications, 341:1 (2008), 188
-
Akian M., Gaubert S., Lakhoua A., “Convergence Analysis of the Max-Plus Finite Element Method for Solving Deterministic Optimal Control Problems”, 47th IEEE Conference on Decision and Control, 2008 (CDC 2008), IEEE Conference on Decision and Control, IEEE, 2008, 927–934
-
Allamigeon X., Gaubert S., Goubault E., “Inferring Min and Max Invariants Using Max-Plus Polyhedra”, Static Analysis, Lecture Notes in Computer Science, 5079, eds. Alpuente M., Vidal G., Springer-Verlag Berlin, 2008, 189–204
-
McEneaney W.M., Deshpande A., Gaubert S., “Curse-of-Complexity Attenuation in the Curse-of-Dimensionality-Free Method for Hjb PDEs”, 2008 American Control Conference, Vols 1-12, Proceedings of the American Control Conference, IEEE, 2008, 4684–4690
-
McEneaney W. M., “Convergence Rate for a Curse-of-dimensionality-Free Method for Hamilton–Jacobi–Bellman PDEs Represented as Maxima of Quadratic Forms”, SIAM J. Control Optim., 48:4 (2009), 2651–2685
-
Akian, M, “THE MAX-PLUS MARTIN BOUNDARY”, Documenta Mathematica, 14 (2009), 195
-
Gaubert, S, “The tropical analogue of polar cones”, Linear Algebra and Its Applications, 431:5–7 (2009), 608
-
Gaubert S., “Max-Plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games”, Formal Modeling and Analysis of Timed Systems, Proceedings, Lecture Notes in Computer Science, 5813, eds. Ouaknine J., Vaandrager F., Springer-Verlag Berlin, 2009, 7–11
-
Fan B., Zhang H., Dou W., “A Max-Plus Network Calculus”, Proceedings of the 8th IEEE/Acis International Conference on Computer and Information Science, eds. Miao H., Hu G., IEEE Computer Soc, 2009, 149–154
-
Mceneaney W.M., Kluberg L.J., “Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of Hjb PDEs”, SIAM J. Control Optim., 48:5 (2009), 3052–3079
-
Akian M., Gaubert S., Guterman A., “Linear Independence Over Tropical Semirings and Beyond”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 1–38
-
Akian M., Gaubert S., Kolokoltsov V., “The Optimal Assignment Problem for a Countable State Space”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 39–60
-
Joswig M., “Tropical Convex Hull Computations”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 193–212
-
McEneaney W.M., “Complexity Reduction, Cornices and Pruning”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 293–303
-
Sergeev S., “Multiorder, Kleene Stars and Cyclic Projectors in the Geometry of Max Cones”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 317–342
-
Shpiz G.B. Litvinov G.L., “A Tropical Version of the Schauder Fixed Point Theorem”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 343–350
-
Fan Baohua, Zhang Heying, Dou Wenhua, “A Matrix Interpretation of Network Calculus”, 2009 First International Conference on Future Information Networks, eds. Zhang H., Coyle E., Kuo S., Zukerman M., IEEE, 2009, 45–49
-
Gaubert S., Meunier F., “Carath,odory, Helly and the Others in the Max-Plus World”, Discrete & Computational Geometry, 43:3 (2010), 648–662
-
М. М. Заричный, “Пространства и отображения идемпотентных мер”, Изв. РАН. Сер. матем., 74:3 (2010), 45–64
; M. M. Zarichnyi, “Spaces and maps of idempotent measures”, Izv. Math., 74:3 (2010), 481–499 -
Nitica V., Sergeev S., “ON HYPERPLANES AND SEMISPACES IN MAX-MIN CONVEX GEOMETRY”, Kybernetika (Prague), 46:3 (2010), 548–557
-
Singer I., “Elementary Topical Functions on B-Complete Semimodules Over B-Complete Idempotent Semifields”, Linear Alg. Appl., 433:11-12 (2010), 2139–2146
-
Ruuge A.E., van Oystaeyen F., “Q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant”, J. Phys. A-Math. Theor., 43:34 (2010), 345203
-
Di Loreto M., Gaubert S., Katz R.D., Loiseau J.-J., “Duality Between Invariant Spaces for Max-Plus Linear Discrete Event Systems”, SIAM J. Control Optim., 48:8 (2010), 5606–5628
-
Gaubert S., McEneaney W., Qu Zh., “Curse of Dimensionality Reduction in Max-Plus Based Approximation Methods: Theoretical Estimates and Improved Pruning Algorithms”, 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-Ecc), IEEE, 2011, 1054–1061
-
Akian M., Gaubert S., Nitica V., Singer I., “Best Approximation in Max-Plus Semimodules”, Linear Alg. Appl., 435:12 (2011), 3261–3296
-
Allamigeon X., Gaubert S., Katz R.D., “Tropical Polar Cones, Hypergraph Transversals, and Mean Payoff Games”, Linear Alg. Appl., 435:7, SI (2011), 1549–1574
-
Nitica V., Sergeev S., “An Interval Version of Separation by Semispaces in Max-Min Convexity”, Linear Alg. Appl., 435:7, SI (2011), 1637–1648
-
Peperko A., “On the Continuity of the Generalized Spectral Radius in Max Algebra”, Linear Alg. Appl., 435:4 (2011), 902–907
-
Gaubert S., Katz R.D., “Minimal Half-Spaces and External Representation of Tropical Polyhedra”, J. Algebr. Comb., 33:3 (2011), 325–348
-
Litvinov G.L., “Tropical Mathematics, Idempotent Analysis, Classical Mechanics and Geometry”, Spectral Theory and Geometric Analysis, Contemporary Mathematics, 535, ed. Braverman M. Friedlander L. Kappeler T. Kuchment P. Topalov P. Weitsman J., Amer Mathematical Soc, 2011, 159–186
-
Allamigeon X., Gaubert S., Katz R.D., “The Number of Extreme Points of Tropical Polyhedra”, J. Comb. Theory Ser. A, 118:1 (2011), 162–189
-
Singer I., Nitica V., “Topical Functions on Semimodules and Generalizations”, Linear Alg. Appl., 437:10 (2012), 2471–2488
-
Bazylevych L., Repovs D., Zarichnyi M., “Hyperspaces of Max-Plus Convex Subsets of Powers of the Real Line”, J. Math. Anal. Appl., 394:2 (2012), 481–487
-
Gaubert S., McEneaney W.M., “Min-Max Spaces and Complexity Reduction in Min-Max Expansions”, Appl. Math. Optim., 65:3 (2012), 315–348
-
Butkovic P., Schneider H., Sergeev S., “Z-Matrix Equations in Max-Algebra, Nonnegative Linear Algebra and Other Semirings”, Linear Multilinear Algebra, 60:10 (2012), 1191–1210
-
Maslov V.P., “New Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts”, Russ. J. Math. Phys., 19:1 (2012), 63–100
-
Akian M., Gaubert S., Guterman A., “Tropical Polyhedra Are Equivalent to Mean Payoff Games”, Int. J. Algebr. Comput., 22:1 (2012), 1250001
-
Allamigeon X., Gaubert S., Goubault E., “Computing the Vertices of Tropical Polyhedra Using Directed Hypergraphs”, Discret. Comput. Geom., 49:2 (2013), 247–279
-
Litvinov G.L., Rodionov A.Ya., Sergeev S.N., Sobolevski A.N., “Universal Algorithms for Solving the Matrix Bellman Equations Over Semirings”, Soft Comput., 17:10 (2013), 1767–1785
-
Shpiz G.B., Litvinov G.L., Sergeev S.N., “On Common Eigenvectors for Semigroups of Matrices in Tropical and Traditional Linear Algebra”, Linear Alg. Appl., 439:6 (2013), 1651–1656
-
Litvinov G.L., “Idempotent and Tropical Mathematics; Complexity of Algorithms and Interval Analysis”, Comput. Math. Appl., 65:10 (2013), 1483–1496
-
Cencelj M., Repovs D., Zarichnyi M., “Max-Min Measures on Ultrametric Spaces”, Topology Appl., 160:5 (2013), 673–681
-
McEneaney W.M., Deshpande A.S., “Payoff Suboptimality and Errors in Value Induced by Approximation of the Hamiltonian”, SIAM J. Control Optim., 51:5 (2013), 3993–4015
-
Katz R.D., Nitica V., Sergeev S., “Characterization of Tropical Hemispaces by (P, R)-Decompositions”, Linear Alg. Appl., 440 (2014), 131–163
-
Fitzpatrick B.G., Holmbeck-Cannell K., Laffin M., Wang Yu., “Optimal Perimeter Patrol Via Max-Plus Probability”, 2014 American Control Conference, Proceedings of the American Control Conference, IEEE, 2014, 5248–5253
-
Allamigeon X., Benchimol P., Gaubert S., Joswig M., “Combinatorial Simplex Algorithms Can Solve Mean Payoff Games”, SIAM J. Optim., 24:4 (2014), 2096–2117
-
Allamigeon X., Fahrenberg U., Gaubert S., Katz R.D., Legay A., “Tropical Fourier-Motzkin Elimination, With An Application To Real-Time Verification”, Int. J. Algebr. Comput., 24:5 (2014), 569–607
-
Singer I., Nitica V., “Extended-Valued Topical and Anti-Topical Functions on Semimodules”, Linear Alg. Appl., 446 (2014), 25–70
-
Allamigeon X., Benchimol P., Gaubert S., Joswig M., “Tropicalizing the Simplex Algorithm”, SIAM Discret. Math., 29:2 (2015), 751–795
-
Dower P.M., Zhang H., “a New Fundamental Solution For Differential Riccati Equations Arising in l-2-Gain Analysis”, 2015 5Th Australian Control Conference (Aucc), IEEE, 2015, 65–68
-
Joswig M., Loho G., “Weighted digraphs and tropical cones”, Linear Alg. Appl., 501 (2016), 304–343
-
Bhuniya A.K., Jana K., “Semigroup of k-bi-Ideals of a Semiring with Semilattice Additive Reduct”, Demonstr. Math., 49:2 (2016), 119–128
-
Akian M., Bapat R., Gaubert S., “Non-archimedean valuations of eigenvalues of matrix polynomials”, Linear Alg. Appl., 498:SI (2016), 592–627
-
Ludkowski S.V., “Skew Continuous Morphisms of Ordered Lattice Ringoids”, 4, no. 1, 2016
-
McEneaney W.M., Pandey A., “An idempotent algorithm for a class of network-disruption games”, Kybernetika, 52:5 (2016), 666–695
-
Barsam H., Mohebi H., “Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions”, Numer. Funct. Anal. Optim., 37:11 (2016), 1354–1377
-
Hassani S., Mohebi H., “Characterizations of minimal elements of topical functions on semimodules with applications”, Linear Alg. Appl., 520 (2017), 104–124
-
Maragos P., “Dynamical Systems on Weighted Lattices: General Theory”, Math. Control Signal Syst., 29:4 (2017), 1
-
Muller V., Peperko A., “On the Bonsall Cone Spectral Radius and the Approximate Point Spectrum”, Discret. Contin. Dyn. Syst., 37:10 (2017), 5337–5354
-
Dower P.M., Zhang H., “A Max-Plus Primal Space Fundamental Solution For a Class of Differential Riccati Equations”, Math. Control Signal Syst., 29:3 (2017), 15
-
Shitov Ya., “Which Semifields Are Exact?”, J. Algebra, 492 (2017), 393–401
-
Allamigeon X., Katz R.D., “Tropicalization of Facets of Polytopes”, Linear Alg. Appl., 523 (2017), 79–101
-
Fijavz M.K., Peperko A., Sikolya E., “Semigroups of Max-Plus Linear Operators”, Semigr. Forum, 94:2 (2017), 463–476
-
Avendano M., Kogan R., Nisse M., Rojas J.M., “Metric Estimates and Membership Complexity For Archimedean Amoebae and Tropical Hypersurfaces”, J. Complex., 46 (2018), 45–65
-
Bhuniya A.K., Jana K., “Representation of Normal Bands as Semigroups of K-Bi-Ideals of a Semiring”, Algebr. Universalis, 79:1 (2018), UNSP 6
-
Legaz-Aparicio A.-G., Verdu-Monedero R., Angulo J., “Adaptive Morphological Filters Based on a Multiple Orientation Vector Field Dependent on Image Local Features”, J. Comput. Appl. Math., 330 (2018), 965–981
-
Komenda J., Lahaye S., Boimond J.-L., van den Boom T., “Max-Plus Algebra in the History of Discrete Event Systems”, Annu. Rev. Control, 45 (2018), 240–249
-
Muller V., Peperko A., “Lower Spectral Radius and Spectral Mapping Theorem For Suprema Preserving Mappings”, Discret. Contin. Dyn. Syst., 38:8 (2018), 4117–4132
-
Gasik M., Zuhlke A., Haaparanta A.-M., Muhonen V., Laine K., Bilotsky Y., Kellomaki M., Kiviranta I., “The Importance of Controlled Mismatch of Biomechanical Compliances of Implantable Scaffolds and Native Tissue For Articular Cartilage Regeneration”, Front. Bioeng. Biotechnol., 6 (2018), 187
-
Tsiamis A., Maragos P., “Sparsity in Max-Plus Algebra and Systems”, Discret. Event Dyn. Syst.-Theory Appl., 29:2 (2019), 163–189
-
Park S., “B-Spaces Are Kkm Spaces”, J. Nonlinear Convex Anal., 20:4 (2019), 739–746
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