Metric regularity and systems of generalized equations

Metric regularity and systems of generalized equations

The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity and metric multi-regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. Th...

System of fuzzy fractional differential equations in generalized metric space

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

Metric regularity of semi-infinite constraint systems

We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F + g is not metrically regular is equa...

Regularity Criteria for the Generalized MHD Equations

Restrictive metric regularity and generalized differential calculus in Banach spaces

We consider nonlinear mappings f :X → Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x̄, that is, metric regularity of f from X into themetric space E = f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves...