and Applied Analysis 3 Remark 1.1. If E is a reflexive strictly convex and smooth Banach space, then for x, y ∈ E, φ x, y 0 if and only if x y. It is sufficient to show that if φ x, y 0 then x y. From 1.6 , we have ‖x‖ ‖y‖. This implies 〈x, Jy〉 ‖x‖2 ‖Jy‖2. From the definitions of j, we have Jx Jy, that is, x y, see 8, 9 for more details. Let C be a nonempty closed convex subset of a smooth Bana...

in this paper, we establish and prove the existence of best proximity points for multivalued cyclic $f$- contraction mappings in complete metric spaces. our results improve and extend various results in literature.

Functional dependencies [4] and multivalued dependencies [5,11] are important, widely-studied constraints on databases. A fundamental issue in database theory is the question of determining whether or not a given set of dependencies (in our case, functional and multivalued dependencies) logically implies another given dependency. We provide a simple and elegant set-theoretic characterization fo...

Recently, the issues of how to define functional dependencies (XFDs) and multivalued dependencies (XMVDs) in XML have been investigated. In this paper we consider the problem of checking the satisfaction of a set of XMVDs in an XML document. We present an algorithm using extensible hashing to check whether an XML document satisfies a given set of XMVDs. The performance of the algorithm is shown...

T h i i work describes tools for generating decision trees that are opt i mized w i th respect to linearity and are more efficient than those generated by Bratko's A O C D L [3] The rule generator is specialized to as to obey stated constraints corresponding to the above two properties. Rule induction takes advantage of one of the expert's most reliable and highly developed skills [9 ] , teachi...

Quality database schemata must capture both the structure and semantics of the domain of interest. Classes of data dependencies have been studied extensively to model domain semantics. Traditionally, the theory of data dependencies has been limited to relations. In practice, duplicate and partial information are permitted to occur in database instances. These features are supported to make data...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

The work of the last two decades on RTDs has been dominated by the needs of semiconductor heterostructure devices for high frequency operation and high speed applications. The fast transit time of the quantum effect involved in the conduction mechanism and the exhibited negative differential resistance have motivated these extensive efforts. The development of the band-gap engineering has opene...

This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied. We show that a unique characterization (encoding) of such multilinear partit...