Set valued mappings, continuous selections, and metric projections

Lower Semicontinuity Concepts, Continuous Selections, and Set Valued Metric Projections

A number of semicontinuity concepts and the relations between them are discussed. Characterizations are given for when the (set-valued) metric projection P M onto a proximinal subspace M of a normed linear space X is approximate lower semicontinuous or 2-lower semicontinuous. A geometric characterization is given of those normed linear spaces X such that the metric projection onto every one-dim...

Σ-products and selections of set-valued mappings

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

Stationary Points for Set-valued Mappings on Two Metric Spaces

We give stationary point theorems of set-valued mappings in complete and compact metric spaces. The results in this note generalize a few results due to Fisher. 2000 Mathematics Subject Classification. 54H25.

Existence theorems for single-valued and set-valued mappings with w-distances in metric spaces

Metric Regularity of Composition Set-valued Mappings: Metric Setting and Coderivative Conditions

The paper concerns a new method to obtain a direct proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the uni…cation and re…nement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years ...