فهرست مطالب
Journal of Linear and Topological Algebra
Volume:5 Issue: 2, Spring 2016
- تاریخ انتشار: 1395/05/11
- تعداد عناوین: 7
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Pages 67-81In this paper, we introduce the notion of multi-fuzzy normed spaces and establish an asymptotic behavior of the quadratic functional equations in the setup of such spaces. We then investigate the superstability of strongly higher derivations in the framework of multi-fuzzy Banach algebrasKeywords: fuzzy normed space, higher derivation, Hyers-Ulam-Rassias stability, multi-normed space, quadratic functional equation
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Pages 83-91In this paper, we define the notion of a bipolar general fuzzy automaton, then we construct some closure operators on the set of states of a bipolar general fuzzy automaton. Also, we construct some topologies on the set of states of a bipolar general fuzzy automaton. Then we obtain some relationships between them.Keywords: Fuzzy automata, closure, operator, bipolar valued fuzzy set
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Pages 93-104In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.Keywords: Common fixed point, $S, b$-metric spaces, compatible mappings, Cauchy sequence
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Pages 105-109For the subclasses $mathcal{M}_1$ and $mathcal{M}_2$ of monomorphisms in a concrete category $mathcal{C}$, if $mathcal{M}_2subseteq mathcal{M}_1$, then $mathcal{M}_1$-injectivity implies $mathcal{M}_2$-injectivity. The Baer type criterion is about the converse of this fact. In this paper, we apply injectivity to the classes of $C$-dense, $C$-closed monomorphisms. The concept of quasi injectivity is also introduced here to investigte the Baer type criterion for these notions.Keywords: $C$-dense injective, $C$-closed injective, quasi-injective
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Pages 111-118We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the category of filters has a left adjoint.Keywords: Universal algebra, topological algebra, nearness spaces, merotopic spaces, filter spaces
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Pages 119-133In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.Keywords: Random fixed point, nonlinear integral random equation, contractively generalized hybrid
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Pages 135-144Let $G$ be a group and $Aut(G)$ be the group of automorphisms of $G$. For any natural number $m$, the $m^{th}$-autocommutator subgroup of $G$ is defined as: $$K_{m} (G)=langle[g,alpha_{1},ldots,alpha_{m}] |gin G,alpha_{1},ldots,alpha_{m}in Aut(G)rangle.$$ In this paper, we obtain the $m^{th}$-autocommutator subgroup of all finite abelian groups.Keywords: Automorphism, Lower autocentral series, Finite Abelian group