Fan’s inequality in geodesic spaces

Abstract

Fan's minimax inequality is extended to the context of metric spaces with global nonpositive curvature. As a consequence, a much more general result on the existence of a Nash equilibrium is obtained.

Some Remarks on Convex Network Flows forK-Spiders

“…See [10]. More pieces of information on global NPC spaces are available in [9,[11][12][13]. We recall the basic convexity notions in a global NPC space.…”

A minimax inequality and its applications to fixed point theorems in CAT(0) spaces

“…The following important result is established in [11]. Theorem 2.1 (KKM mapping principle) Suppose that E is a complete CAT(0) space with the convex hull finite property and X is a nonempty subset of E. Furthermore, suppose M : X 2 X is a KKM mapping with closed values.…”

“…Definition 2.1 [11] Let C be a nonempty subset of a CAT(0) space E. A multivalued mapping G : C 2 E is said a KKM mapping if…”

A Good Earthquake Concave Behaviour of a Seismic Isolator Which Supports a Metallic Roof

“…See [1]. More details on global NPC spaces are available in [2][3][4][5]. In the following sentences we define the basic convexity notions in a global NPC space.…”

“…A simple consequence is that the convex hull of subset of a -spider is also a -spider included in . Based on the fact that the closed convex hull of every nonempty finite family of points of has the fixed point property in [4] the Schauder fixed point theorem has been proved. Definition 6.…”