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## Generalizations of Hyperconvex Metric Spaces

#### Sehei Park [1]

Since Khamsi found a KKM theorem for hyperconvex metric spaces in 1996, there have appeared a large number of works on them related to the KKM theory.  In our previous review [34], we followed the various stages of developments of the  KKM theory of hyperconvex metric spaces. In fact, we introduced abstracts of articles on such theory and gave comments or generalizations of the results there if necessary. We noted that many results in those articles are consequences of  (partial) KKM space theory developed by ourselves from 2006. The present survey is a continuation of [34] and aims to collect further generalizations of hyperconvex metric spaces related to the KKM theory.

convex space, Generalizations of Hyperconvex Metric Spaces, abstract convex space; Horvath space, metric type space, metric spaces with continuous midpoints, global nonpositive curvature (NPC)
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• 30] Park, S. Generalizations of the Nash equilibrium theorem in the KKM theory, Takahashi Legacy, Fixed Point Theory Appl. vol. 2010, Article ID 234706, 23pp. doi:10.1155 /2010/234706.
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• [35] S. Park, Comments on the KKM theory of metric type spaces, Linear and Nonlinear Anal. 2(1)(2016), 39--45.[36] S. Park, Generalizations of Khamsi's KKM and fi xed point theorems on hyperconvex metric spaces,Nonlinear Anal. Forum 22(2) (2017), 7--15.
• [37] S. Park, A history of the KKM Theory, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 56(2) (2017), 1--51.
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• 39] S. Park, A panoramic view of the KKM theory on abstract convex spaces, J. Nat. Acad. Sci., ROK,Nat. Sci. Ser. 57(2) (2018), 1--46.
• [40] S. Park, From Hadamard manifolds to Horvath spaces, J. Nat. Acad. Sci., ROK, Nat. Sci. Ser. 58(1)(2019), 1--36.
• [41] S. Park, Extending the realm of Horvath spaces, J. Nonlinear Convex Anal. (Takahashi Issue)
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• [43] D. Turkoglu, M. Abuloha, and T. Abdeljawad, KKM mappings in cone metric spaces and some xed point theorems, Nonlinear Anal. 72 (2010), 348--353. doi:10.1016/j.na.2009.06.058.
Primary Language en Mathematics Articles Author: Sehei Park (Primary Author)Institution: The National Academy of Sciences, Republic of KoreaCountry: South Korea Publication Date : August 30, 2019
 Bibtex @research article { rna573805, journal = {Results in Nonlinear Analysis}, issn = {}, eissn = {2636-7556}, address = {}, publisher = {Erdal KARAPINAR}, year = {2019}, volume = {2}, pages = {71 - 82}, doi = {}, title = {Generalizations of Hyperconvex Metric Spaces}, key = {cite}, author = {Park, Sehei} } APA Park, S . (2019). Generalizations of Hyperconvex Metric Spaces. Results in Nonlinear Analysis , 2 (2) , 71-82 . Retrieved from https://dergipark.org.tr/en/pub/rna/issue/45041/573805 MLA Park, S . "Generalizations of Hyperconvex Metric Spaces". Results in Nonlinear Analysis 2 (2019 ): 71-82 Chicago Park, S . "Generalizations of Hyperconvex Metric Spaces". Results in Nonlinear Analysis 2 (2019 ): 71-82 RIS TY - JOUR T1 - Generalizations of Hyperconvex Metric Spaces AU - Sehei Park Y1 - 2019 PY - 2019 N1 - DO - T2 - Results in Nonlinear Analysis JF - Journal JO - JOR SP - 71 EP - 82 VL - 2 IS - 2 SN - -2636-7556 M3 - UR - Y2 - 2019 ER - EndNote %0 Results in Nonlinear Analysis Generalizations of Hyperconvex Metric Spaces %A Sehei Park %T Generalizations of Hyperconvex Metric Spaces %D 2019 %J Results in Nonlinear Analysis %P -2636-7556 %V 2 %N 2 %R %U ISNAD Park, Sehei . "Generalizations of Hyperconvex Metric Spaces". Results in Nonlinear Analysis 2 / 2 (August 2019): 71-82 . AMA Park S . Generalizations of Hyperconvex Metric Spaces. RNA. 2019; 2(2): 71-82. Vancouver Park S . Generalizations of Hyperconvex Metric Spaces. Results in Nonlinear Analysis. 2019; 2(2): 82-71.