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Numerical Functional Analysis and Optimization Volume 20, 1999 - Issue 5-6
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Original Articles

Continuous Selection Theorems in Generalized Convex Spaces

Sehie Park Department of Mathematics, Seoul National University, Seoul, 151-742, Korea
Pages 567-583 | Published online: 15 May 2007

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Read on this site (3)

Nguyen Xuan Tan. (2018) Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings. Numerical Functional Analysis and Optimization 39:2, pages 233-255.
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S. Jafari, A. P. Farajzadeh, S. Moradi & P. Q. Khanh. (2017) Existence results for -quasimonotone equilibrium problems in convex metric spaces. Optimization 66:3, pages 293-310.
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Xie Ping Ding & Jong Yeoul Park. (2002) COLLECTIVELY FIXED POINT THEOREM AND ABSTRACT ECONOMY IN G-CONVEX SPACES. Numerical Functional Analysis and Optimization 23:7-8, pages 779-790.
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Articles from other publishers (56)

Marco Castellani & Massimiliano Giuli. (2022) A Modified Michael’s Selection Theorem with Application to Generalized Nash Equilibrium Problem. Journal of Optimization Theory and Applications 196:1, pages 199-211.
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Haishu Lu, Xiaoqiu Liu & Rong Li. (2022) Upper semicontinuous selections for fuzzy mappings in noncompact $ WPH $-spaces with applications. AIMS Mathematics 7:8, pages 13994-14028.
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Bhagwati Prasad Chamola, Ritu Sahni & Manoj Sahni. 2022. Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy. Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy 77 91 .
M. Ali Khan & Metin Uyanik. (2021) The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications. Economic Theory 71:3, pages 799-840.
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Haishu Lu, Kai Zhang & Rong Li. (2021) Collectively fixed point theorems in noncompact abstract convex spaces with applications. AIMS Mathematics 6:11, pages 12422-12459.
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Sehie PARK. (2020) The rise and fall of L-spaces. Advances in the Theory of Nonlinear Analysis and its Application 4:3, pages 152-166.
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Zoran D. Mitrović, Azhar Hussain, Manuel de la Sen & Stojan Radenović. (2020) On Best Approximations for Set-Valued Mappings in G -convex Spaces. Mathematics 8:3, pages 347.
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Haishu Lu & Qingwen Hu. (2013) A Collectively Fixed Point Theorem in Abstract Convex Spaces and Its Applications. Journal of Function Spaces and Applications 2013, pages 1-10.
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Min Fang & Xie Ping Ding. (2013) A New Fixed Point Theorem and Applications. Abstract and Applied Analysis 2013, pages 1-5.
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Sehie Park. (2011) Applications of some basic theorems in the KKM theory. Fixed Point Theory and Applications 2011:1.
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P. Q. Khanh, V. S. T. Long & N. H. Quan. (2011) Continuous Selections, Collectively Fixed Points and Weak Knaster–Kuratowski–Mazurkiewicz Mappings in Optimization. Journal of Optimization Theory and Applications 151:3, pages 552-572.
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Somyot Plubtieng & Tipphawan Thammathiwat. (2011) Existence of solutions of systems of generalized implicit vector quasi-equilibrium problems in -convex spaces . Computers & Mathematics with Applications 62:1, pages 124-130.
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Ming-ge Yang & Lei Deng. (2010) Coincidence theorem for admissible set-valued mappings and its applications in FC-spaces. Acta Mathematicae Applicatae Sinica, English Series 26:3, pages 455-462.
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Sehie Park. (2010) Generalizations of the Nash Equilibrium Theorem in the KKM Theory. Fixed Point Theory and Applications 2010:1.
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Sehie Park. (2010) Comments on abstract convexity structures on topological spaces. Nonlinear Analysis: Theory, Methods & Applications 72:2, pages 549-554.
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Hoon-Joo Kim. (2009) GENERALIZED MINIMAX THEOREMS IN GENERALIZED CONVEX SPACES. Honam Mathematical Journal 31:4, pages 559-578.
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Haishu Lu. (2009) Continuous Selection and Fixed Point Theorems for Fuzzy Mappings in General Topological Spaces. Continuous Selection and Fixed Point Theorems for Fuzzy Mappings in General Topological Spaces.
Sehie Park. (2009) Fixed point theory of multimaps in abstract convex uniform spaces. Nonlinear Analysis: Theory, Methods & Applications 71:7-8, pages 2468-2480.
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Haishu Lu. (2009) Continuous Selection Theorems and Fixed Point Theorems for Fuzzy Mappings in FC-Spaces. Continuous Selection Theorems and Fixed Point Theorems for Fuzzy Mappings in FC-Spaces.
Qing-bang Zhang, Ming-jie Liu & Cao-zong Cheng. (2009) Generalized saddle points theorems for set-valued mappings in locally generalized convex spaces. Nonlinear Analysis: Theory, Methods & Applications 71:1-2, pages 212-218.
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Ming-Ge Yang & Lei Deng. (2009) Equilibria of nonparacompact generalized games with -majorized correspondences in FC-spaces. Nonlinear Analysis: Theory, Methods & Applications 70:2, pages 890-903.
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Władysław Kulpa & Andrzej Szymanski. (2007) Applications of General Infimum Principles to Fixed-Point Theory and Game Theory. Set-Valued Analysis 16:4, pages 375-398.
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Sehie Park. (2008) Compact Browder maps and equilibria of abstract economies. Journal of Applied Mathematics and Computing 26:1-2, pages 555-564.
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Sehie Park. (2007) A Unified Fixed Point Theory in Generalized Convex Spaces. Acta Mathematica Sinica, English Series 23:8, pages 1509-1526.
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Xieping Ding. (2007) System of generalized vector quasi-equilibrium problems on product FC-spaces. Acta Mathematica Scientia 27:3, pages 522-534.
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Xie Ping Ding. (2007) Collective fixed points and a system of coincidence theorems in product -spaces and applications. Nonlinear Analysis: Theory, Methods & Applications 66:11, pages 2604-2617.
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Zoran D. Mitrović. (2007) On scalar equilibrium problem in generalized convex spaces. Journal of Mathematical Analysis and Applications 330:1, pages 451-461.
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Sehie Park. (2007) Fixed point theorems for better admissible multimaps on almost convex sets. Journal of Mathematical Analysis and Applications 329:1, pages 690-702.
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Qing-bang Zhang & Cao-zong Cheng. (2007) Some fixed-point theorems and minimax inequalities in FC-space. Journal of Mathematical Analysis and Applications 328:2, pages 1369-1377.
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Xie Ping Ding. (2006) Nonempty Intersection Theorems and Generalized Multi-objective Games in Product FC-Spaces. Journal of Global Optimization 37:1, pages 63-73.
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Xie Ping Ding. (2006) Continuous Selection, Collectively Fixed Points and System of Coincidence Theorems in Product Topological Spaces. Acta Mathematica Sinica, English Series 22:6, pages 1629-1638.
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Zoran D Mitrović. (2006) On almost coincidence points in generalized convex spaces. Fixed Point Theory and Applications 2006:1.
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Xie Ping Ding. (2006) System of Generalized Vector Quasi–Equilibrium Problems in Locally FC–Spaces. Acta Mathematica Sinica, English Series 22:5, pages 1529-1538.
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Xie Ping Ding. (2006) Weak Pareto equilibria for generalized constrained multiobjective games in locally -spaces. Nonlinear Analysis: Theory, Methods & Applications 65:3, pages 538-545.
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Ming-ge Yang & Lei Deng. (2006) Continuous selection theorems for Fan-Browder mappings in topological spaces and their applications. Applied Mathematics and Mechanics 27:4, pages 493-500.
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Mircea Balaj. (2006) Two minimax inequalities in -convex spaces . Applied Mathematics Letters 19:3, pages 235-239.
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Sehie Park. (2006) COINCIDENCE THEOREMS ON $\omega$-CONNECTED SPACES. Taiwanese Journal of Mathematics 10:2.
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Z. D. Mitrović. (2006) Remarks on Best Approximations in Generalized Convex Spaces. Journal of Applied Analysis 12:2.
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Lai-Jiu Lin, Ngai-Ching Wong & Zenn-Tsuen Yu. (2005) Continuous selections and fixed points of multi-valued mappings on noncompact or nonmetrizable spaces. Proceedings of the American Mathematical Society 133:11, pages 3421-3427.
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Cai-Yun Jin & Cao-Zong Cheng. (2005) S-G-L-KKM theorems in L-convex space and their applications to minimax inequalities. Computers & Mathematics with Applications 50:1-2, pages 123-131.
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Xieping Ding. (2005) COINCIDENCE THEOREMS IN PRODUCT G -CONVEX SPACES. Acta Mathematica Scientia 25:3, pages 401-407.
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Mircea Balaj. (2009) Minimax inequalities in G -convex spaces . Bulletin of the Australian Mathematical Society 71:3, pages 367-376.
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Xie Ping Ding. (2005) Maximal element theorems in product FC-spaces and generalized games. Journal of Mathematical Analysis and Applications 305:1, pages 29-42.
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Sehie Park. (2005) Comments on collectively fixed points in generalized convex spaces. Applied Mathematics Letters 18:4, pages 431-437.
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Ding Xie-ping. (2004) Nonempty intersection theorems and system of generalized vector equilibrium problems in product G-convex spaces. Applied Mathematics and Mechanics 25:6, pages 618-626.
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Jeong-Heon Kim & Sehie Park. (2004) Comments on some fixed point theorems in hyperconvex metric spaces. Journal of Mathematical Analysis and Applications 291:1, pages 154-164.
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K.Q. Lan. (2004) New fixed-point theorems for two maps and applications to problems on sets with convex sections and minimax inequalities. Computers & Mathematics with Applications 47:2-3, pages 195-205.
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Ding Xie-ping. (2003) Maximal elements forG B-majorized mappings in productG-convex spaces and applications (I). Applied Mathematics and Mechanics 24:6, pages 659-672.
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Xie Ping Ding & Jong Yeoul Park. (2003) Collectively fixed-point theorems in noncompact G-convex spaces. Applied Mathematics Letters 16:2, pages 137-142.
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H.-L. Zhang. (2003) Some Nonlinear Problems in Hyperconvex Metric Spaces. Journal of Applied Analysis 9:2.
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Zenn-Tsuen Yu & Lai-Jiu Lin. (2003) Continuous selection and fixed point theorems. Nonlinear Analysis: Theory, Methods & Applications 52:2, pages 445-455.
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Xie Ping Ding, Jong Yeoul Park & Il Hyo Jung. (2002) Existence of solutions for nonlinear inequalities in G-convex spaces. Applied Mathematics Letters 15:6, pages 735-741.
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Xie Ping Ding & J.Y. Park. (2002) Continuous selection theorem, coincidence theorem, and generalized equilibrium in L-convex spaces. Computers & Mathematics with Applications 44:1-2, pages 95-103.
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K.Q. Lan & J.H. Wu. (2002) A fixed-point theorem and applications to problems on sets with convex sections and to Nash equilibria. Mathematical and Computer Modelling 36:1-2, pages 139-145.
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Sehie Park. (2002) Remarks on equilibria for g-monotone maps on generalized convex spaces. Journal of Mathematical Analysis and Applications 269:1, pages 244-255.
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Sehie Park. (2002) Fixed point theorems in locally G-convex spaces. Nonlinear Analysis: Theory, Methods & Applications 48:6, pages 869-879.
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