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Khan, Suhel Ahmad; Shehu, Yekini; Chen, J. W.

Gap functions and existence of solution of simultaneous equilibrium problems. (English) Zbl 1368.49007

Afr. Mat. 28, No. 1-2, 249-261 (2017).
Summary: In this paper, we propose some new gap functions for simultaneous vector equilibrium problems without any scalarization parameters which are computationally easier than previously known methods in the literature. Further, we give the notion of a \(P\)-monotone family of mappings and prove the existence of solutions of simultaneous vector equilibrium problems by using a fixed-point theorem in a Hausdorff topological vector space. Furthermore, we give sufficient conditions for the upper semicontinuity of the solution set of the parametric problem corresponding to the simultaneous vector equilibrium problems.

MSC:

49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
47H10 Fixed-point theorems
90C99 Mathematical programming
49J45 Methods involving semicontinuity and convergence; relaxation

Keywords:

simultaneous vector equilibrium problems; gap function; \(P\)-monotone family of mappings; \(v\)-hemicontinuous mapping
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References:

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