in the present paper‎, ‎we introduce the concept of generalized multivalued $f$ -‎contraction mappings and give a fixed point result‎, ‎which is a proper‎ ‎generalization of some multivalued fixed point theorems including nadler's‎.

Applications of the fixed point theory of multivalued maps can be classified into several areas: (1) Game theory and mathematical economics; (2) Discontinuous differential equations and differential inclusions; (3) Computing homology of maps; (4) Conley index methods in chaotic dynamics; (5) Digital imaging and computer vision. We briefly recall the history of the most classical and well develo...

In this paper, a new segmentation technique for multivalued images is elaborated. The technique accesses multiscale edge information of a multivalued image by a concept, called multiscale fundamental form. At different scales, an edge map of the multivalued images is obtained, at which a watershed-based algorithm is applied. The multiscale behavior of the obtained watershed regions is employed ...

The discrete dynamics generated by a continuous map can be represented combinatorially by an appropriate multivalued map on a discretization of the phase space such as a cubical grid or triangulation. In this paper we provide explicit algorithms and computational complexity bounds for computing dynamical structures for the resulting combinatorial multivalued maps. Specifically we focus on the c...

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 ...

Consider a relation schema with a set of dependency constraints. A fundamental question is what is the minimum space where the possible instances of the schema can be ”stored”. We study the following model. Encode the instances by giving a function which maps the set of possible instances into the set of words of a given length over the binary alphabet in a decodable way. The problem is to find...

This paper presents a new algorithm for planning the time-optimal motion of a robot traveling with limited velocity from a given location to a given destination on a surface in the presence of moving obstacles. Additional constraints such as space variant terrain traversability and fuel economy can be accommodated. A multivalued distance map is defined and applied in computing optimal trajector...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Abstract In this paper, the existence of solutions for differential inclusions of fractional order q ∈ (1, 2] with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not ...

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...

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...