Multivalued projections are applied to the study of weighted least squares solutions linear relations equations (or inclusions) and some its applications. To this end a matrix representation multivalued with respect closure their ranges is described.

The study of fixed points of single-valued self-mappings or multivalued self-mappings satisfying certain contraction conditions has a great majority of results inmetric fixed point theory. All these results are mainly generalizations of Banach contraction principle. The Banach contraction principle guarantees the existence and uniqueness of fixed points of certain self-maps in complete metric s...

We consider the modeling approach introduced by R. Thomas for the qualitative study of gene regulatory networks. Tools and results on regulatory networks are often concerned only with the Boolean case of this formalism. However, multivalued approaches are sometimes more suited to model biological situations. Multivalued networks can be converted to partial Boolean maps, in a way that preserves ...

Nesting of relations is very much essential for many database representations in reality. Nesting of relations tends to reduce the data redundancy in the relations. It helps in dropping certain constraints in normalization which tend to omit certain sensitive data when tried to be normalized. Query processing or conversion of data repositories, as required, can be easily being tackled by the ai...

We establish a general fixed point theorem for multivalued maps defined on cones in Banach spaces. Applications to single and multivalued equations are presented. 2000 Mathematics Subject Classification: 47H10, 45M20.

Functional dependencies, a notion originated in Relational Database Theory, are known to admit interesting characterizations in terms of Formal Concept Analysis. In database terms, two successive, natural extensions of the notion of functional dependency are the socalled degenerate multivalued dependencies, and multivalued dependencies proper. We propose here a new Galois connection, based on a...

The study of fixed points for multivalued contractions and nonexpansive maps using the Hausdorff metric was initiated by Markin [17]. Later, an interesting and rich fixed point theory for such maps has been developed. The theory of multivalued maps has applications in control theory, convex optimization, differential inclusions, and economics (see, e.g., [3, 8, 16, 22]). The theory of multivalu...

In this paper, we introduce a new class of bifunction variational inequalities, which is called the multivalued mixed quasi bifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the multivalued mixed quasi bifunction variational inequalities. It is shown that the convergence of the proposed method requires only p...

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how th...