# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Fan’s inequality in geodesic spaces. (English) Zbl 1171.26332
Summary: 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.
##### MSC:
 26D15 Inequalities for sums, series and integrals of real functions
Full Text:
##### References:
 [1] Borwein, J. M.; Lewis, A. S.: Convex analysis and nonlinear optimization. Theory and examples, (2000) · Zbl 0953.90001 [2] Bridson, M. R.; Haefliger, A.: Metric spaces of non-positive curvature, Grundlehren der mathematischen wissenschaften 319 (1999) · Zbl 0988.53001 [3] Ballmann, W.: Lectures on spaces with nonpositive curvature, DMV seminar 25 (2005) [4] Jost, J.: Nonpositive curvature: geometric and analytic aspects, Lectures in mathematics ETH Zürich (1997) · Zbl 0896.53002 [5] Sturm, K. T.: Probability measures on metric spaces of nonpositive curvature, Contemp. math. 338, 357-390 (2003) · Zbl 1040.60002 [6] Niculescu, C. P.; Rovenţa, I.: Fan’s inequality in the context of mp-convexity, Applied analysis and differential equations (Proc. ICAADE 2006), 267-274 (2007) · Zbl 1194.49012 [7] Lytchak, A.; Schroeder, V.: Affine functions on $Cat(k)$ spaces, Math. Z. 255, 231-244 (2007) · Zbl 1197.53044 · doi:10.1007/s00209-006-0020-4