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Main purpose of this paper is to combine the optimal form of Fan's
best approximation theorem and Nash's equilibrium existence theorem
into a single existence theorem simultaneously.
For this, we first prove a general best proximity pair theorem which
includes a number of known best proximity theorems. Next, we will
introduce a new equilibrium concept for a generalized Nash game with
normal form, and as applications, we will prove new existence
theorems of Nash equilibrium pairs for generalized Nash games with
normal form.
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참고문헌 (24)
참고문헌 신청
G. Beer / 1990 / Proximal maps, prox maps and coincidence points / Numerical Functional Analysis and Optimization 11 (5) : 429 ~ 448
G. Debreu / 1952 / A social equilibrium existence theorem / Proc. Nat. Acad. Sci. U. S. A. : 886 ~ 893
H. Nikaid?o / 1955 / Note on non-cooperative convex games / Pacific Journal of Mathematics 5 : 807 ~ 815
I. Jo´o / 1986 / Answer to a problem of M. Horv´ath and A. S¨ovegj´art´o / Annales Universitatis Scientarium Budapestinensis de Rolando Eotvos Nominatae Sectio Mathemat
I. Singer / 1970 / Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces / Springer-Verlag
G. Debreu / 1952 / A social equilibrium existence theorem / Proc. Nat. Acad. Sci. U. S. A. : 886 ~ 893
H. Nikaid?o / 1955 / Note on non-cooperative convex games / Pacific Journal of Mathematics 5 : 807 ~ 815
I. Jo´o / 1986 / Answer to a problem of M. Horv´ath and A. S¨ovegj´art´o / Annales Universitatis Scientarium Budapestinensis de Rolando Eotvos Nominatae Sectio Mathemat
I. Singer / 1970 / Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces / Springer-Verlag
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