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About 10,000 papers for “strong continuity”

Soft strong $ \theta $-continuity and soft almost strong $ \theta $-continuity

Dina Abuzaid, Samer Al-Ghour · AIMS Mathematics · 2024

<abstract><p>We continued the study of "soft strong $ \theta $-continuity" and defined and investigated "soft almost strong $ \theta $-continuity" which is a generalization of soft strong $ \theta $-continuity. We gave characterizations and examined soft composition concerning these two concepts. Furthermore, we derived several soft mapping theorems. We provided several links between these two ideas and their related concepts through examples. Lastly, we looked at the symmetry between them and their topological counterparts.</p></abstract>

Cited by 1Open access

Strong Proximal Continuity and Convergence

Agata Caserta, Roberto Lucchetti, Som Naimpally · Abstract and Applied Analysis · 2013

In several situations the notion of uniform continuity can be strengthened to strong uniform continuity to produce interesting properties, especially in constrained problems. The same happens in the setting of proximity spaces. While a parallel theory for uniform and strong uniform convergence was recently developed, and a notion of proximal convergence is present in the literature, the notion of strong proximal convergence was never considered. In this paper, we propose several possible convergence notions, and we provide complete comparisons among these concepts and the notion of strong uniform convergence in uniform spaces. It is also shown that in particularly meaningful classes of functions these notions are equivalent and can be considered as natural definitions of strong proximal convergence. Finally we consider a function acting between two proximity spaces and we connect its continuity/strong continuity to convergence in the respective hyperspaces of a natural functor associated to the function itself.

Cited by 1Open access

Strong continuity on Hardy spaces

Jacek Dziubański, Błażej Wróbel · arXiv (Cornell University) · 2016

We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson semigroups as well as the group of imaginary powers.

Cited by 0Open access

On almost strong θ-continuity

Mohammed Saleh · 2015

P. E. Long and D. A. Carnahan in [6] and Noiri in [10] studied several prop-erties of a.c.S, a.c.H and weak continuity. In this paper it is shown that results similar to those in the above mentioned papers still hold for θ-continuity and strong θ-continuity. Furthermore, several decomposition theorems of θ-continuity and strong θ-continuity are obtained. 1

Cited by 0

Strong continuity on Hardy spaces

Jacek Dziubański, Błażej Wróbel · arXiv (Cornell University) · 2016

We prove the strong continuity of spectral multiplier operators associated with dilations of certain functions on the general Hardy space $H^1_L$ introduced by Hofmann, Lu, Mitrea, Mitrea, Yan. Our results include the heat and Poisson semigroups as well as the group of imaginary powers.

Cited by 0Open access

Strongly Proximal Continuity \& Strong Connectedness

James F. Peters, C. Guadagni · arXiv (Cornell University) · 2015

This article introduces strongly proximal continuous (s.p.c.) functions, strong proximal equivalence (s.p.e.) and strong connectedness. A main result is that if topological spaces $X,Y$ are endowed with compatible strong proximities and $f:X\longrightarrow Y$ is a bijective s.p.e., then its extension on the hyperspaces $\CL(X)$ and $\CL(Y)$, endowed with the related strongly hit and miss hypertopologies, is a homeomorphism. For a topological space endowed with a strongly near proximity, strongly proximal connectedness implies connectedness but not conversely. Conditions required for strongly proximal connectedness are given. Applications of s.p.c. and strongly proximal connectedness are given in terms of strongly proximal descriptive proximity.

Cited by 3Open access

Some Remarks on Closure and Strong Continuity

Mohammad Saleh · An-Najah University Journal for Research - A (Natural Sciences) · 1998

Noire studied several properties of weak continuity in Proc. Amer. Math. Soc. 46(1), 120-124. In this paper it is shown that similar to most of the results of the above paper still hold for closure and strong continuity. Example 2 is a counterexample to a corollary to Theorem 6 of Long and Herrington. Theorem 12 of our paper is a sharper result to Theorem 5 of Noire. Several decomposition theorems of closure and strong continuity are obtained.

Cited by 1Open access

On the strong continuity of generalised semigroups

Raj Dahya · arXiv (Cornell University) · 2020

It is well known that weakly continuous semigroups defined over $\mathbb{R}_{+}$ are automatically strongly continuous. We extend this result to more generally defined semigroups, including multiparameter semigroups.

Cited by 2Open access

On strong continuity of derivatives of mappings

Durdil, J. · Czech digital mathematics library · 1986

Relations between strong continuity of derivatives and uniformity of differentiability of mappings in locally convex spaces are studied; results are formulated for families of mappings.V prci je vyetovna souvislost mezi zeslenou spojitost derivac a stejnomrnou diferencovatelnost zobrazen v lokln konvexnch prostorech; vsledky jsou formulovny pro systmy zobrazen.

Cited by 0Open access