Acta et Commentationes Universitatis Tartuensis de Mathematica

By a Fréchet algebra, we mean a complete metrizable locally convex topological algebra. The boundedness of a set in Fréchet algebras is of course a topological property, but the uniform bound of a uniformly bounded set is an algebraic property, since it depends on the choice of seminorms generating the same topology on Fréchet algebra. In this paper, we show that if S is a bounded subsemigroup of a Fréchet algebra (A; (pn)n∈N), then there is an equivalent family of seminorms (tn)n∈N on A, such that tn(s)≤1 (s∈S; n∈N). In the rest of this paper, we get a result by using this fact, and we also have a discussion on continuous inverse algebras.

Esmaeil Ansari-Piri

Banafsheh Fattahi-Solaymandarabi

On the algebraic property of locally convex topological algebras

关于局部凸拓扑代数的代数性质

I-convergence is a type of convergence that generalizes many known types of convergences. In this study, I-convergence and I-boundedness of multiset sequences are defined and some examples are given. I-limit points, I-cluster points, Bmx and Amx sets and the concepts of I-limit infimum and I-limit supremum are defined for a multiset sequence. These definitions are supported by examples. It is shown that the set of I-cluster points of a multiset sequence covers the set of I-limit points and I-lim inf mx ≤ I-lim sup mx. Additionally, necessary and sufficient conditions for I-lim inf mx = I-lim sup mx are proved.

Hafize Gümüş

Nihal Demir

I-limit points and I-cluster points of multiset sequences

多重集序列的I-极限点和I-聚点

The investigation of Yamabe solitons within almost contact metric manifolds has garnered significant interest recently, producing notable findings. This paper aims to explore the inverse problem: constructing almost contact metric structures on a three-dimensional Riemannian manifold endowed with an almost Yamabe soliton. Subsequently, we provide the techniques required to characterize the nature of these structures, accompanied by concrete examples.

Gherici Beldjilali

Adel Delloum

From Yamabe to almost contact metric structure

从山田到近似接触度量结构

Modified third-order Jacobsthal quaternion sequence is defined in this study. Some properties involving this sequence, including the Binet-style formula and the generating function are presented.

Gamaliel Morales

A note on modified third-order Jacobsthal quaternions and their properties

关于修正的三阶雅可比四元数及其性质的注记

In this paper, we introduce a new family of Lucas quaternions by using finite operators. We call these quaternions as Lucas finite operator quaternions. We give some properties and identities of Lucas finite operator quaternions such as Binet-like formula, generating function, exponential generating function, Catalan's identity, Cassini's identity, d'Ocagne's identity and many binomial-sum identities. As an application, we generate Cassini's identity in another form by matrix representations.

Abbreviation
Journal Impact	0.35
Quartiles(Global)	MATHEMATICS(Q4)

Publication Information	Publisher: Tartu University Press，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2014，Proportion of original research papers: 100.00%，Self Citation Rate:33.30%， Gold OA Rate: 96.88%

Acta et Commentationes Universitatis Tartuensis de Mathematica

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On the algebraic property of locally convex topological algebras

I-limit points and I-cluster points of multiset sequences

From Yamabe to almost contact metric structure

A note on modified third-order Jacobsthal quaternions and their properties

A new generalization of Lucas quaternions with finite operators

On the algebraic property of locally convex topological algebras

I-limit points and I-cluster points of multiset sequences

From Yamabe to almost contact metric structure

A note on modified third-order Jacobsthal quaternions and their properties

A new generalization of Lucas quaternions with finite operators

ISSN	1406-2283, 2228-4699
h-index	9