Advances in Operator Theory

Existence results for approximate set-valued equilibrium problems

Malek Abbasi and Mahboubeh Rezaei

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This paper studies the generalized approximate set-valued equilibrium problems and furnishes some new existence results. The existence results for solutions are derived by using the celebrated KKM theorem and some concepts associated with the semi-continuity of the set-valued mappings such as outer-semicontinuity, inner-semicontinuity, upper-semicontinuity and so forth. The results achieved in this paper generalize and improve the works of many authors in references.

Article information

Adv. Oper. Theory, Volume 1, Number 2 (2016), 189-205.

Received: 16 October 2016
Accepted: 13 December 2016
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 49J40: Variational methods including variational inequalities [See also 47J20]
Secondary: 90C33: Complementarity and equilibrium problems and variational inequalities (finite dimensions) 90C26: Nonconvex programming, global optimization 91B50: General equilibrium theory

set-valued equilibrium problems KKM theorem outersemicontinuity inner-semicontinuity set-convergence


Abbasi, Malek; Rezaei, Mahboubeh. Existence results for approximate set-valued equilibrium problems. Adv. Oper. Theory 1 (2016), no. 2, 189--205. doi:10.22034/aot.1610.1034.

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