فهرست مطالب
Journal of Linear and Topological Algebra
Volume:9 Issue: 1, Winter 2020
- تاریخ انتشار: 1398/12/11
- تعداد عناوین: 7
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Pages 1-15
In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternative theorem. Moreover, we investigate Hyers-Ulam-Rassias stability of generalized $C^*$-ternary derivation for such function on $C^*$-algebras by the same method.
Keywords: Cauchy-Jensen functional equations, Hyers-Ulam-Rassias stability, C*-ternary algebras, alternative fixed point theorem -
Pages 17-34In this paper, we first introduce some types of generalized $alpha$-Meir-Keeler contractions in $b$-metric-like spaces and then we establish some fixed point results for these types of contractions. Also, we present a new fixed point theorem for a Meir-Keeler contraction through rational expression. Finally, we give some examples to illustrate the usability of the obtained results.Keywords: $alpha$-admissible, fixed point, Meir-Keeler contraction, $b$-metric-like
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Pages 35-51The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces by using an analogue theorem of Brzdc{e}k in [17].Keywords: Stability, hyperstability, 2-Banach spaces, radical functional equation
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Pages 53-65In this paper, we introduce the concept of Su-type contractive mapping and establish fixed point theorems for such mappings in the setting of ordered extended partial $b$-metric space. We also develop an application for Fredholm type integral equations to validate our main result and a non-trivial example is given to elucidate our work.Keywords: Altering distance function, Su-type contraction, extended partial $b$-metric space, integral equation
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Pages 67-74The aim of this paper is to establish the equivalence between the concepts of an $S$-metric space and a cone $S$-metric space using some topological approaches. We introduce a new notion of a $TVS$-cone $S$-metric space using some facts about topological vector spaces. We see that the known results on cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained from the studies on $S$-metric spaces.Keywords: S-metric, cone S-metric, N-cone metric
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Pages 75-94The aim of this paper is to establish and prove some results on common fixed point for a pair of multi-valued mappings in complex valued $b$-metric spaces. Our results generalize and extend a few results in the literature.Keywords: fixed point, Common fixed point, multi-valued mappings, complex valued $b$-metric spaces
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Pages 95-103In this paper, we prove that the category of crossed polymodules (i.e. crossed modules of polygroups) and their morphisms is finitely complete. We, therefore, generalize the group theoretical case of this completeness property of crossed modules.Keywords: Polygroup, crossed module, Limit