On generalized equilibrium points

Kas, P.; Kassay, G.; Sensoy, Zehra Boratas

doi:10.1016/j.jmaa.2004.04.030

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New Existence Results For Equilibria On Compact Sets1

Introduction1

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Cited by 9 publications

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“…To this purpose, we introduce a definition of approximate equilibrium point, for both cases (see [9] for a definition of approximate equilibrium for functions defined on product spaces). We start our analysis with (EP).…”

Section: New Existence Results For Equilibria On Compact Setsmentioning

confidence: 99%

Existence of equilibria via Ekeland's principle

Bianchi

Kassay

Pini

2005

Journal of Mathematical Analysis and Applications

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In the literature, when dealing with equilibrium problems and the existence of their solutions, the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity, together with some weak continuity assumptions, of the function. In this paper, we focus on conditions that do not involve any convexity concept, neither for the domain nor for the function involved. Starting from the well-known Ekeland's theorem for minimization problems, we find a suitable set of conditions on the function f that lead to an Ekeland's variational principle for equilibrium problems. Via the existence of -solutions, we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems.  2004 Elsevier Inc. All rights reserved.

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Section: New Existence Results For Equilibria On Compact Setsmentioning

confidence: 99%

Existence of equilibria via Ekeland's principle

Bianchi

Kassay

Pini

2005

Journal of Mathematical Analysis and Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…There were many papers dealing with perturbed convex programs, for instance, [1], [4], [5], [6], [8], [11], [21], [22], [23], [24], [26], and [27]. A common feature of them is that the perturbed functionf is assumed to remain convex.…”

Section: Introductionmentioning

confidence: 99%