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Journal articles on the topic 'Fan theorem'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Wen, Kai Ting. "A Matching Theorem in FC-Spaces with the Application to Coincidence Questions." Applied Mechanics and Materials 204-208 (October 2012): 4766–70. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.4766.

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A Ky Fan type matching theorem for weakly transfer compactly open valued mappings is established in FC-spaces. As applications, Fan–Browder type fixed point theorems and Ky Fan type coincidence theorems are obtained in FC-spaces.

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2

Park, Sehie. "On minimax inequalities on spaces having certain contractible subsets." Bulletin of the Australian Mathematical Society 47, no. 1 (1993): 25–40. http://dx.doi.org/10.1017/s0004972700012235.

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The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.

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3

Darzi, Rahmat, Rostamian Delavar, and Mehdi Roohi. "Fixed point theorems in minimal generalized convex spaces." Filomat 25, no. 4 (2011): 165–76. http://dx.doi.org/10.2298/fil1104165d.

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This paper deals with coincidence and fixed point theorems in minimal generalized convex spaces. By establishing a kind of KKM Principle in minimal generalized convex space, we obtain some results on coincidence point and fixed point theorems. Generalized versions of Ky Fan?s lemma, Fan-Browder fixed point theorem, Nash equilibrium theorem and some Urai?s type fixed point theorems in minimal generalized convex spaces are given.

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4

Karamikabir, Nasrin, and Abdolrahman Razani. "Some KKM theorems in modular function spaces." Filomat 28, no. 7 (2014): 1307–13. http://dx.doi.org/10.2298/fil1407307k.

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In this paper, a coincidence theorem is obtained which is generalization of Ky Fan?s fixed point theorem in modular function spaces. A modular version of Fan?s minimax inequality is proved. Moreover, some best approximation theorems are presented for multi-valued mappings.

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5

KO, HWEI-MEI, and KOK-KEONG TAN. "A NOTE ON A COVERING THEOREM OF KY FAN." Tamkang Journal of Mathematics 22, no. 4 (1991): 329–33. http://dx.doi.org/10.5556/j.tkjm.22.1991.4618.

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   A covering theorem by open sets is proved to be equivalent to a covering theorem by closed sets due to Ky Fan. DuaI theorems of Shapley zmd Knaster et al. are obtained as applications.   

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6

VELDMAN, WIM. "ON SOME OF BROUWER’S AXIOMS." Bulletin of Symbolic Logic 31, no. 1 (2025): 1–52. https://doi.org/10.1017/bsl.2024.52.

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AbstractWe argue that some of Brouwer’s assumptions, rejected by Bishop, should be considered and studied as possible axioms. We show that Brouwer’s Continuity Principle enables one to prove an intuitionistic Borel Hierarchy Theorem. We also explain that Brouwer’s Fan Theorem is useful for a development of the theory of measure and integral different from the one worked out by Bishop. We show that Brouwer’s bar theorem not only proves the Fan Theorem but also a stronger statement that we call the Almost-fan Theorem. The Almost-fan Theorem implies intuitionistic versions of Ramsey’s Theorem and

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7

Jafari, F., and V. M. Sehgal. "Some fixed point theorems for nonconvex spaces." International Journal of Mathematics and Mathematical Sciences 21, no. 1 (1998): 133–37. http://dx.doi.org/10.1155/s0161171298000179.

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We give a theorem for nonconvex topological vector spaces which yields the classical fixed point theorems of Ky Fan, Kim, Kaczynski, Kelly and Namioka as immediate consequences, and prove a new fixed point theorem for set-valued maps on arbitrary topological vector spaces.

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8

Valentini, Silvio. "Generalising the fan theorem." Mathematical Logic Quarterly 63, no. 1-2 (2017): 85–93. http://dx.doi.org/10.1002/malq.201500016.

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9

LUBARSKY, ROBERT S., and HANNES DIENER. "SEPARATING THE FAN THEOREM AND ITS WEAKENINGS." Journal of Symbolic Logic 79, no. 3 (2014): 792–813. http://dx.doi.org/10.1017/jsl.2014.9.

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AbstractVarieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.

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10

Li, He Rui, and Kai Ting Wen. "Ky Fan Matching Theorems for MFC Mappings in FC-Metric Spaces with the Application to Minimax Inequalities." Advanced Materials Research 838-841 (November 2013): 2219–22. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.2219.

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In this paper, MFC mappings is introduced and Ky Fan matching theorems for MFC mappings with transfer compactly open values are established in noncompact complete FC-metric spaces. As applications, a Fan-Browder type coincidence theorem and a minimax inequality are obtained. Our results unify, improve and generalize some known results in recent literature.

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11

KO, HWEI-MEI, and KOK-KEONG TAN. "COINCIDENCE THEOREMS AND MATCHING THEOREMS." Tamkang Journal of Mathematics 23, no. 4 (1992): 297–309. http://dx.doi.org/10.5556/j.tkjm.23.1992.4553.

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   Two coincidence theorems of Ky Fan are first slightly generalized. As applications, new matching theorems are obtained, one of which has several equivalent forms, including the classical Knaster Kuratowski-Mazurkiewicz theorem.   

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12

Tang, Gusheng, та Qingbang Zhang. "Class𝔄-KKM(X,Y,Z), GeneralKKMType Theorems, and Their Applications in Topological Vector Space". Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/238191.

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The class𝔄-KKM(X,Y,Z)and generalizedKKMmapping are introduced, and some generalizedKKMtheorems are proved. As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.

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13

Chen, Yi-An, and Yi-Ping Zhang. "A Class of Fan-Browder Type Fixed-Point Theorem and Its Applications in Topological Space." Abstract and Applied Analysis 2010 (2010): 1–9. http://dx.doi.org/10.1155/2010/314616.

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A fixed-point theorem is proved under noncompact setting of general topological spaces. By applying the fixed-point theorem, several new existence theorems of solutions for equilibrium problems are proved under noncompact setting of topological spaces. These theorems improve and generalize the corresponding results in related literature.

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14

Li, Jinlu. "Some Eigenvector Theorems Proved by a Fan–KKM Theorem." Journal of Mathematical Analysis and Applications 263, no. 2 (2001): 738–47. http://dx.doi.org/10.1006/jmaa.2001.7657.

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15

Ding, Xie Ping, Won Kyu Kim, and Kok-Keong Tan. "A new minimax inequality on H-spaces with applications." Bulletin of the Australian Mathematical Society 41, no. 3 (1990): 457–73. http://dx.doi.org/10.1017/s0004972700018347.

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A new minimax inequality on H-spaces is obtained together with six equivalent formulations. As applications, some results on fixed point theorems and system of inequalities are proved. Our results generalise the corresponding results on (1) minimax inequalities due to Fan, Yen, Tan, Shih-Tan and Ding-Tan, (2) fixed point theorems due to Browder, Tarafdar, Shih-Tan and Ding-Tan, (3) convex inequalities due to Fan, (4) systems of inequalities due to Granas-Liu and (5) a minimax theorem due to Kneser.

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16

BERGER, JOSEF, and GREGOR SVINDLAND. "BROUWER’S FAN THEOREM AND CONVEXITY." Journal of Symbolic Logic 83, no. 04 (2018): 1363–75. http://dx.doi.org/10.1017/jsl.2018.49.

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AbstractIn the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of ${\left\{ {0,1} \right\}^{\rm{*}}}$, the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of ${\left\{ {0,1} \right\}^{\rm{*}}}$ and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f sat

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17

Ding, Xie-Ping. "Continuous selection theorem, coincidence theorem and intersection theorems concerning sets with H-convex sections." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, no. 1 (1992): 11–25. http://dx.doi.org/10.1017/s1446788700032833.

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AbstractA continuous selection and a coincidence theorem are proved in H-spaces which generalize the corresponding results of Ben-El-Mechaiekh-Deguire-Granas, Browder, Ko-Tan, Lassonde, Park, Simon and Takahashi to noncompact and/or nonconvex settings. By applying the two theorems, some intersection theorems concerning sets with H-convex sections are obtained which generalize the corresponding results of Fan, Lassonde and Shih-Tan to H-spaces. Some applications to minimax principle are given.

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18

Wen, Kai Ting, and He Rui Li. "An RS-KKM Theorem in FC-Metric Spaces with the Application to Fixed Points." Advanced Materials Research 838-841 (November 2013): 2215–18. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.2215.

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In this paper, RS-KKM mappings are introduced and an RS-KKM theorem is established in noncompact complete FC-metric spaces. As applications, a Ky Fan section theorem, a maximal element theorem and a Fan-Browder type fixed point theorem are obtained in noncompact complete FC-metric spaces. These results unify, improve and generalize some known results in recent literature.

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19

Tarafdar, E. "Fixed point theorems in H-spaces and equilibrium points of abstract economies." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 2 (1992): 252–60. http://dx.doi.org/10.1017/s1446788700035825.

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AbstractSome fixed point theorems on H-spaces are presented. These theorems are then applied to generalize a theorem of Fan concerning sets with convex sections to H-spaces and to prove the existence of equilibrium points of abstract economics in which the commodity space is an H-space.

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20

Ha, Chung-Wei. "On a homotopy invariant for simplexes and its application." Bulletin of the Australian Mathematical Society 55, no. 1 (1997): 73–80. http://dx.doi.org/10.1017/s0004972700030549.

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Based on a congruence relation of K. Fan in the integer labelling of pseudomanifolds, we follow an idea of H. Sies and define a mod 2 homotopy invariant d for a class of continuous functions defined on an n-simplex into ℝn+1 ＼ {0} satisfying a certain boundary condition. Using the homotopy invariance of d, generalised coincidence theorems are proved which unify and extend some existence theorems of K. Fan. Our results also contain Kakutani's fixed point theorem and a new covering property of simplexes of Shapley's type.

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21

Roohi, Mehdi, and Mohsen Rostamian Delavar. "On F-implicit Minimal Vector Variational Inequalities." Statistics, Optimization & Information Computing 10, no. 2 (2022): 401–9. http://dx.doi.org/10.19139/soic-2310-5070-434.

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In this paper, by introducing some new concepts in minimal spaces, we prove a generalized form of the Fan-KKM theorem in minimal vector spaces. A new class of minimal generalized vector F-implicit variational inequality problems and, as an application of Fan-KKM theorem is investigated. Moreover, an existence theorem for this kind of problems under some suitable assumptions in minimal vector spaces is given.

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22

Diener, Hannes, and Peter Schuster. "On Choice Principles and Fan Theorems." JUCS - Journal of Universal Computer Science 16, no. (18) (2010): 2556–62. https://doi.org/10.3217/jucs-016-18-2556.

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Veldman proved that the contrapositive of countable binary choice is a theorem of full-fledged intuitionism, to which end he used a principle of continuous choice and the fan theorem. It has turned out that continuous choice is unnecessary in this context, and that a weak form of the fan theorem suffices which holds in the presence of countable choice. In particular, the contrapositive of countable binary choice is valid in Bishop-style constructive mathematics. We further discuss a generalisation of this result and link it to Ishihara's boundedness principle BD-N.

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23

Tanaka, Yasuhito. "Brouwer's Fixed Point Theorem with Isolated Fixed Points and His Fan Theorem." ISRN Computational Mathematics 2012 (January 26, 2012): 1–3. http://dx.doi.org/10.5402/2012/843256.

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24

Cobos, Fernando. "On a theorem of Ky Fan." Colloquium Mathematicum 55, no. 2 (1988): 249–51. http://dx.doi.org/10.4064/cm-55-2-249-251.

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25

Saito, Akira. "Fan-type theorem for path-connectivity." Combinatorica 16, no. 3 (1996): 433–37. http://dx.doi.org/10.1007/bf01261327.

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26

Loeb, Iris. "Equivalents of the (Weak) Fan Theorem." Annals of Pure and Applied Logic 132, no. 1 (2005): 51–66. http://dx.doi.org/10.1016/j.apal.2004.07.002.

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27

Hu, Zhiquan, Feng Tian, Bing Wei, Yoshimi Egawa, and Kazuhide Hirohata. "Fan-type theorem for path-connectivity." Journal of Graph Theory 39, no. 4 (2002): 265–82. http://dx.doi.org/10.1002/jgt.10028.

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28

Panina, G., and R. Živaljević. "Ky Fan Theorem for Sphere Bundles." Russian Journal of Mathematical Physics 32, no. 1 (2025): 141–49. https://doi.org/10.1134/s1061920825600138.

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29

Ahmad, Rais, and Mijanur Rahaman. "Generalized strongly vector equilibrium problem for set-valued mappings." Filomat 28, no. 9 (2014): 1783–90. http://dx.doi.org/10.2298/fil1409783a.

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In this paper, we introduce and study a generalized strongly vector equilibrium problem for set-valued mappings in real Banach spaces. Using Minty type lemma and KKM-Fan theorem as basic tools, we prove existence theorems for generalized strongly vector equilibrium problem with and without monotonicity, respectively. Some examples are given.

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30

Sy, Polly W., and Sehie Park. "The KKM maps and fixed point theorems in convex spaces." Tamkang Journal of Mathematics 34, no. 2 (2003): 169–74. http://dx.doi.org/10.5556/j.tkjm.34.2003.264.

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From a general form of the celebrated Knaster--Kuratowski--Mazurkiewicz (simply, KKM) theorem, we deduce a new form of the Fan--Browder fixed point theorem, an approximate fixed point theorem, and the Himmelberg fixed point theorem.

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31

Fujiwara, Makoto, and Tatsuji Kawai. "Decidable fan theorem and uniform continuity theorem with continuous moduli." Mathematical Logic Quarterly 67, no. 1 (2021): 116–30. http://dx.doi.org/10.1002/malq.202000028.

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32

Yuan, George Xian-Zhi. "Fixed points of upper semicontinuous mappings in locally G-convex spaces." Bulletin of the Australian Mathematical Society 58, no. 3 (1998): 469–78. http://dx.doi.org/10.1017/s0004972700032457.

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In this paper a new fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values is established in the setting of an abstract convex structure – called a locally G-convex space, which generalises usual convexity such as locally convex H-spaces, locally convex spaces (locally H-convex spaces), hyperconvex metric spaces and locally convex topological spaces. Our fixed point theorem includes corresponding Fan-Glicksberg type fixed point theorems in locally convex H-spaces, locally convex spaces, hyperconvex metric space and locally convex spaces in the existing lite

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33

Watson, P. J. "Coincidences and fixed points in locally G-convex spaces." Bulletin of the Australian Mathematical Society 59, no. 2 (1999): 297–304. http://dx.doi.org/10.1017/s0004972700032901.

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A new coincidence point theorem is proved for a pair of multivalued mappings operating between G-convex spaces. From this theorem, a generalisation of the classical Fan-Glicksberg fixed point theorem is established.

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34

Tarafdar, E. "A fixed point theorem in H-space and related results." Bulletin of the Australian Mathematical Society 42, no. 1 (1990): 133–40. http://dx.doi.org/10.1017/s0004972700028239.

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The equivalence of a fixed point theorem and the Fan-Knaster-Kuratowski-Mazurkiewicz theorem in H-space has been established. The fixed point theorem is then applied to obtain a theorem on sets with H-convex sections, and also results on minimax inequalities.

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35

Berger, Josef. "Constructive Equivalents of the Uniform Continuity Theorem." JUCS - Journal of Universal Computer Science 11, no. (12) (2005): 1878–83. https://doi.org/10.3217/jucs-011-12-1878.

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For the purpose of constructive reverse mathematics, we show the equivalence of the uniform continuity theorem to a series of propositions; this illuminates the relationship between Brouwer's fan theorem and the uniform continuity theorem

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36

Hai, Nguyen Xuan, and Nguyen Van Hung. "On the existence of solutions for vector quasiequilibrium problems." Tạp chí Khoa học 15, no. 3 (2019): 48. http://dx.doi.org/10.54607/hcmue.js.15.3.145(2018).

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In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixed-point theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

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37

Lin, Tzu-Chu. "Convex sets, fixed points, variational and minimax inequalities." Bulletin of the Australian Mathematical Society 34, no. 1 (1986): 107–17. http://dx.doi.org/10.1017/s000497270000455x.

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Recently, Ky Fan extended his will known lemma (which is an extension of the classical theorem of Knaster, Kuratowski and Mazurkiewica) to the noncompact case. Using this result, another interesting lemma of Fan is generalized in this paper. As applications of our theorem, we obtain a generalizationof Browder's variational inequality and derive Fan's other recent results directly from our theorem. Also, in this paper, we give a slight extension recent results of K. K. Tan, which themselves are generalizations of many well-known results on minimax and variational inequalities.

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38

Ding, Xie Ping. "New generalisations of an H-KKM type theorem and their applications." Bulletin of the Australian Mathematical Society 48, no. 3 (1993): 451–64. http://dx.doi.org/10.1017/s0004972700015914.

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In this note, we establish some new generalisations of an H-KKM type theorem which unify and generalise the corresponding results of Horvath, Bardaro-Ceppitelli, Tarafdar, Shioji, Park and others. As applications of our H-KKM type principle, we obtain some new generalisations of the Ky Fan type geometric properties of. H-spaces, minimax inequalities and coincidence theorems in Horvath's abstract setting.

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39

Zhang, Le, and Chuanfeng Sun. "A generalized minimax theorem for sup-concave functionals." Journal of Physics: Conference Series 2898, no. 1 (2024): 012020. http://dx.doi.org/10.1088/1742-6596/2898/1/012020.

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40

Kılıçman, Adem, Rais Ahmad, and Mijanur Rahaman. "Existence Results for Strong Mixed Vector Equilibrium Problem for Multivalued Mappings." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/497846.

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We consider a strong mixed vector equilibrium problem in topological vector spaces. Using generalized Fan-Browder fixed point theorem (Takahashi 1976) and generalized pseudomonotonicity for multivalued mappings, we provide some existence results for strong mixed vector equilibrium problem without using KKM-Fan theorem. The results in this paper generalize, improve, extend, and unify some existence results in the literature. Some special cases are discussed and an example is constructed.

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41

Szűcs, Zsolt. "On Lomonosov’s Lemma in normed spaces." Studia Scientiarum Mathematicarum Hungarica 48, no. 1 (2011): 116–21. http://dx.doi.org/10.1556/sscmath.2010.1158.

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42

Berger, Josef, Douglas Bridges, and Peter Schuster. "The fan theorem and unique existence of maxima." Journal of Symbolic Logic 71, no. 2 (2006): 713–20. http://dx.doi.org/10.2178/jsl/1146620167.

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AbstractThe existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

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43

Zhao, Kewen. "A new short proof of Fan Theorem." Journal of Discrete Mathematical Sciences and Cryptography 16, no. 2-03 (2013): 163–65. http://dx.doi.org/10.1080/09720529.2013.802406.

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44

Gutman, Ivan, Enide A. Martins, María Robbiano, and Bernardo San Martín. "Ky Fan theorem applied to Randić energy." Linear Algebra and its Applications 459 (October 2014): 23–42. http://dx.doi.org/10.1016/j.laa.2014.06.051.

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45

Gerhold, Stefan, and Benedict Bauer. "THE FAN–TAUSSKY–TODD INEQUALITIES AND THE LUMER–PHILLIPS THEOREM." Journal of Inequalities and Special Functions 15, no. 1 (2024): 23–30. https://doi.org/10.54379/jiasf-2024-1-3.

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We argue that a classical inequality due to Fan, Taussky and Todd (1955) is equivalent to the dissipativity of a Jordan block. As the latter can be characterised via the zeros of Chebyshev polynomials, we obtain a short new proof of the inequality. Three other inequalities of Fan–Taussky–Todd are reproven similarly. By the Lumer–Phillips theorem, the matrix semigroup generated by the Jordan block is contractive. This yields new extensions of the classical Fan–Taussky–Todd inequalities. As applications, we give an estimate for the partial sums of a Bessel function, and a contribution to the cla

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46

Ismail, Sumarno, Isran K. Hasan, Tesya Sigar, and Salmun K. Nasib. "RAINBOW CONNECTION NUMBER AND TOTAL RAINBOW CONNECTION NUMBER OF AMALGAMATION RESULTS DIAMOND GRAPH(〖Br〗_4) AND FAN GRAPH(F_3)." BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, no. 1 (2022): 023–30. http://dx.doi.org/10.30598/barekengvol16iss1pp023-030.

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If be a graph and edge coloring of G is a function , rainbow connection number is the minimum-k coloration of the rainbow on the edge of graph G and denoted by rc(G). Rainbow connection numbers can be applied to the result of operations on some special graphs, such as diamond graphs and fan graphs. Graph operation is a method used to obtain a new graph by combining two graphs. This study performed amalgamation operations to obtain rainbow connection numbers and rainbow-total-connection numbers in diamond graphs ( ) and fan graphs ( ) or . Based on the research, it is obtained that the rainbow-

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47

Khushbu and Zubair Khan. "Extended f-Vector Equilibrium Problem." International Journal of Computational Mathematics 2014 (December 3, 2014): 1–6. http://dx.doi.org/10.1155/2014/643230.

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We introduce and study extended f-vector equilibrium problem. By using KKM-Fan Theorem as basic tool, we prove existence theorem in the setting of Hausdorff topological vector space and reflexive Banach space. Some examples are also given.

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48

Tarafdar, E. "A fixed point theorem equivalent to the Fan-Knaster-Kuratowski-Mazurkiewicz theorem." Journal of Mathematical Analysis and Applications 128, no. 2 (1987): 475–79. http://dx.doi.org/10.1016/0022-247x(87)90198-3.

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49

HATTORI, AKIO, and MIKIYA MASUDA. "ELLIPTIC GENERA, TORUS ORBIFOLDS AND MULTI-FANS." International Journal of Mathematics 16, no. 09 (2005): 957–98. http://dx.doi.org/10.1142/s0129167x05003181.

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Multi-fan is an analogous notion of fan in toric theory. Fan is a combinatorial object associated to a toric variety. Multi-fan is associated to an orbifold with an action of half the dimension of the orbifold. In this paper the equivariant elliptic genus and the equivariant orbifold elliptic genus of multi-fans are defined and their character formulas are exhibited. A vanishing theorem concerning elliptic genus of multi-fans of global type and its applications to toric varieties are given.

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50

Eplett, W. J. R. "A fixed point approach to local minimax theory." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 2 (1986): 339–46. http://dx.doi.org/10.1017/s0305004100064252.

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AbstractThe generalized Neyman-Pearson theorem for constructing robust hypothesis tests proved by Huber and Strassen is obtained here as an application of the Kakutani-Fan fixed point theorem. The same technique is applied to obtain the existence of locally minimax estimators.

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