Equilibrium and Quasi-Equilibrium Problems under φ-Quasimonotonicity and φ-Quasiconvexity. Existence, Stability and Applications
Keywords:
Clarkesubdifferential,Clarkegeneralizedderivative,Clarke-Rockafellar subdiffer ential, eigenvalues equilibriumpoints, eigenvaluesminimizers, equilibriumproblems,Minty equilibriumproblems,fixedpoints,Lipschitzfunctions,parametricperturbation,penalization, φ-quasiconvexity,quasi-equilibriumproblems,φ-quasimonotonicity,quasi-optimization,quan titativestability, quasiconvexprogramming, quasi-optimization, Stampacchiavariational and quasi-variational inequalities.Abstract
We introduce a further generalization of quasimonotonicity of real-valued bifunctions and quasiconvexity of real-valued functions what we call φ-quasimonotonicity and φ-quasiconvexity respectively, φ being a bivariate function under appropriate conditions. Our generalization is on the one hand motivated by several counter-examples and examples such as the Clarke Rockafellar directional derivative, and on the other hand includes the weak or relaxed and strong counterparts of these concepts and moreover leads to new definitions of generalized quasicon vexity and quasimonotonicity
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