let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

This paper presents a linear representation of the built environment called “continuity line”. A continuity line is the aggregation of several axial lines to represent an urban path in its longest extension, respecting a maximum sinuosity previously defined. It is based on two main arguments: first, that the notion of continuity is already embedded in the axial system; and second, that the cont...

Al-Hawary [1] introduced and explored the class of ζ−open sets which is strictly weaker than open and proved that the collection of all ζ−open subsets of a space forms a topology that is finer than the original one. In this paper, we introduce what we call ζ−continuity and ζX−continuity and we give several characterizations and two decompositions of ζ−continuity. Finally, new decompositions of ...

A characteriation of continuity of the $p$-$Lambda$-variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of Waterman-Shiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.

In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

In the present article we discuss approximation properties of genuine Lupac{s}-Beta operators of  integral type. We establish quantitative asymptotic formulae and a direct estimate in terms of Ditzian-Totik modulus of continuity. Finally we mention  results on the weighted modulus of continuity for the genuine operators.

1.3. De nition. ABSTRACT. We apply enriched category theory to study Cauchy completeness in continuity spaces. Our main result is the equivalence in continuity spaces of the category theoretic and the uniform notions of Cauchy completeness. This theorem, which generalizes a result of Lawvere for quasi-metric spaces, makes a natural connection between the category-theoretic and topological aspec...

BACKGROUND The traditional concept of continuity of care, i.e. care from the cradle to the grave, is no longer sustainable in modern society. OBJECTIVE The aim of this study was to propose a definition of 'continuity of care' based on the experiences of a group of practising Australian GPs. METHOD Five focus group discussions were conducted to explore the understanding and practice of conti...

Utterances that are close in time are more likely to share the same referent. A word learner who is using information about the speaker’s intended referents should be able to take advantage of this continuity and learn words more efficiently by aggregating information across multiple utterances. In the current study we use corpus data to explore the continuity of reference in caregivers’ speech...