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.

Let 2 be a finite set of join dependencies (JDs), multivalued dependencies (MVDs) and functional dependencies (IDS). To test whether .% implies an MVD X -+ Y or an PD X -+ A, the procedure in [ 31 first generates the dependency basis DEP( X) of X with respect to 2. Then, X + Y if and only if Y is the union of some elements in DEP( X) , and X -+ A if and only if A E DEP( X), and there is an PD V...

We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the unrestricted implication problem for inclusion, functional, and embedded multivalued dependencies in the unirelational case.

There is a well-known algorithm for determining when a decomposition ˆ {R1,R2, . . . ,Rm} of a database relation scheme has a lossless join with respect to a set of functional dependencies. We ®rst present a reformulation of this algorithm in terms of set closures. For the special case of mˆ 2, there is a well-known explicit condition for losslessness. Our formulation extends this result for ge...

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 introduces a new definition of fuzzy multivalued dependency, called α-fmvd, on the basis of the αequality of tuples as defined in [1]. Next the definition is shown to be consistent, i.e., it reduces to that of classical multivalued dependency (mvd) when the choice parameter takes the value one. Finally, a set of sound and complete inference axioms have been designed and proved for th...

The existence of approximate fixed points and approximate endpoints of the multivalued almost I-contractions is established. We also develop quantitative estimates of the sets of approximate fixed points and approximate endpoints for multivalued almost I-contractions. The proved results unify and improve recent results of Amini-Harandi 2010 , M. Berinde and V. Berinde 2007 , Ćirić 2009 , M. Păc...