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المقاله
1 - 2-Banach stability results for the radical cubic functional equation related to quadratic mappingJournal of Linear and Topological Algebra , العدد 1 , السنة 9 , زمستان 2020The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadraticfunctional equation$$f\left(\sqrt[3]{ax^{3}+by^{3}}\right)+f\left(\sqrt[3]{ax^{3}-by^{3}}\right)=2a^{2}f(x)+2b^{2}f(y),\;\; x,y\in\mathbb{R},$$for a map أکثرThe aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadraticfunctional equation$$f\left(\sqrt[3]{ax^{3}+by^{3}}\right)+f\left(\sqrt[3]{ax^{3}-by^{3}}\right)=2a^{2}f(x)+2b^{2}f(y),\;\; x,y\in\mathbb{R},$$for a mapping $f$ from $\mathbb{R}$ into a vector space.We also investigate some stability and hyperstability results forthe considered equation in 2-Banach spaces by using an analogue theorem of Brzd\c{e}k in [17]. تفاصيل المقالة -
المقاله
2 - $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modulesJournal of Linear and Topological Algebra , العدد 1 , السنة 7 , زمستان 2018In this paper, we introduce the concepts of $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules and we establish some results.In this paper, we introduce the concepts of $\ast$-K-g-Frames in Hilbert $\mathcal{A}$-modules and we establish some results. تفاصيل المقالة -
المقاله
3 - A new type of Hyers-Ulam-Rassias stability for Drygas functional equationJournal of Linear and Topological Algebra , العدد 5 , السنة 7 , پاییز 2018In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brz\c{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equ أکثرIn this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brz\c{d}ek's fixed point theorem. Moreover, we give a general result on the hyperstability of this equation. Our results are improvements and generalizations of the main result of M. Piszczek and J. Szczawi\'{n}ska [21]. تفاصيل المقالة -
المقاله
4 - Generalized hyperstability of the cubic functional equation in ultrametric spacesJournal of Linear and Topological Algebra , العدد 2 , السنة 8 , بهار 2019In this paper, we present thegeneralized hyperstability results of cubic functional equation inultrametric Banach spaces using the fixed point method.In this paper, we present thegeneralized hyperstability results of cubic functional equation inultrametric Banach spaces using the fixed point method. تفاصيل المقالة -
المقاله
5 - Operator frame for $End_{\mathcal{A}}^{\ast}(\mathcal{H})$Journal of Linear and Topological Algebra , العدد 2 , السنة 8 , بهار 2019Frames generalize orthonormal bases and allow representation of all the elements of the space. Frames play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicin أکثرFrames generalize orthonormal bases and allow representation of all the elements of the space. Frames play significant role in signal and image processing, which leads to many applications in informatics, engineering, medicine, and probability. In this paper, we introduce the concepts of operator frame for the space $End_{\mathcal{A}}^{\ast}(\mathcal{H})$ of all adjointable operators on a Hilbert $\mathcal{A}$-module $\mathcal{H}$ and establish some results. تفاصيل المقالة