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 establish existence and uniqueness results for a new class of boundary value problems involving the ?-Hilfer generalized proportional fractional derivative operator, supplemented with mixed nonlocal conditions including multipoint, integral multiorder operators. The given problem is first converted into an equivalent fixed point problem, which then solved by means standard the...

In this paper, we establish some sufficient conditions for the existence of a solution equilibrium problem. The problem is understood in general form: find $ \overline{x}\in E such that$ \begin{equation*} \Phi(\overline{x},y) \vartriangleleft (-D\backslash\{0\})^c \text{ all }y \in E; \end{equation*} $and its variants, where Boolean-valued bifunction and \Phi multivalued mapping with values vec...

ÐPhotographic volumes present a unique, interesting challenge for volume rendering. In photographic volumes, voxel color is predetermined, making color selection through transfer functions unnecessary. However, photographic data does not contain a clear mapping from the multivalued color values to a scalar density or opacity, making projection and compositing much more difficult than with tradi...

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...

In this paper, a new segmentation technique for multivalued images is elaborated. The technique makes use of the first fundamental form to access edge information of a multivalued image. On the obtained edge map, a watershedbased algorithm is applied. In order to remove noise or local texture, before segmentation, an anisotropic diffusion filter is applied, also making use of the first fundamen...

In this paper we develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions. These objects have a wide range of applications in optimization, nonlinear analysis, mathematical economics, etc. Our main concern is Lipschitzian stability of multivalued solution maps depending on parameters. We employ a new approach of nonsmooth...