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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:
26D15Inequalities for sums, series and integrals of real functions
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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