Orbital $\varphi$-regularity in coincidence and fixed point problems in metric spaces

The purpose of the present paper is to establish some (approximate) fixed point or coincidence theorems for set-valued mappings defined on metric spaces under the so-called orbital \varphi-regularity of the considered mappings. This is a type of (\varphi,\gamma)-regularity of set-valued mappings which is weaker than orbital regularity. In turn, it is used in the previous … Read more

Directional H”older metric subregularity and application to tangent cones

In this work, we study directional versions of the H\”olderian/Lipschitzian metric subregularity of multifunctions. Firstly, we establish variational characterizations of the H\”olderian/Lipschitzian directional metric subregularity by means of the strong slopes and next of mixed tangency-coderivative objects . By product, we give second-order conditions for the directional Lipschitzian metric subregularity and for the directional metric … Read more