Fréchet quasidifferential calculus with applications to metric regularity of continuous maps

A strong variant for the notion of quasidifferentiability of functions is considered in the light of recent achievements in variational analysis. Several characterization results, some calculus rules and examples are provided. Then a generic result for the corresponding subdifferentiability notion is established in general Banach spaces. Subsequently, such notion is employed in the study of generalized differential criteria for metric regularity. Necessary and sufficient conditions, along with a precise estimation of the norm of metric regularity, are obtained in the case of continuous maps between Banach spaces via a strong slope approach. All these results do not require Asplundity assumptions.