Contents ........................................................ 5
1 Introduction ................................................. 7
2 Preliminaries ............................................... 11
3 Extending mappings .......................................... 15
3.1 A Hahn-Banach-type theorem ............................. 15
3.2 Hyperconvexity and retractions ......................... 25
4 Hyperconvex geometry ........................................ 29
4.1 Basic properties and examples .......................... 29
4.2 Admissible sets ........................................ 30
4.3 Baillon's intersection theorem ......................... 33
4.4 Making hyperconvex spaces .............................. 41
4.5 Hyperconvexity and Banach spaces ....................... 48
4.6 Hyperconvex hull ....................................... 53
4.7  -trees ................................................ 66
5 Fixed points ................................................ 73
5.1 Baillon's fixed point theorem .......................... 73
5.2 Schauder-type fixed-point theorem ...................... 75
5.3 Krasnoselskii-type fixed-point theorem ................. 77
5.4 Darbo-Sadovskii-type fixed-point theorem ............... 79
5.5 Mönch-type fixed-point theorem ......................... 83
5.6 Leray-Schauder-type fixed-point theorem ................ 85
6 Multivalued mappings in hyperconvex spaces .................. 93
6.1 Basic notions .......................................... 93
6.2 Selection theorems ..................................... 94
6.3 Fixed point theorems ................................... 98
Bibliography .................................................. 103
Index of symbols and notions .................................. 107
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