Metric Subregularity and Calmness for Nonconvex Generalized Equations in Banach Spaces

Metric Subregularity and Constraint Qualifications for Convex Generalized Equations in Banach Spaces

Several notions of constraint qualifications are generalized from the setting of convex inequality systems to that of convex generalized equations. This is done and investigated in terms of the coderivatives and the normal cones, and thereby we provide some characterizations for convex generalized equations to have the metric subregularity. As applications, we establish formulas of the modulus ...

Error Bounds and Metric Subregularity

Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued functions of two variables. A classification scheme for the general error bound and metric subregularity criteria is presented. The criteria are formulated i...

Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics First-Order Characterizations of Metric Subregularity and Calmness of Constraint Set Mappings

A condition ensuring metric subregularity (respectively calmness) of general multifunctions between Banach spaces is derived. In finite dimensions this condition can be expressed in terms of a derivative which appears to be a combination of the coderivative and the contingent derivative. It is further shown that this sufficient conditions is in some sense the weakest possible first-order condit...

Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces