Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101A new type of Hyers-Ulam-Rassias stability for Drygas functional equation251260542801ENM. SirouniDepartment of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, MoroccoM. AlmahalebiDepartment of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, MoroccoS. KabbajDepartment of Mathematics, Faculty of Science, Ibn Tofail University, BP-14000, Kenitra, MoroccoJournal Article20171226In this paper, we prove the generalized Hyers-Ulam-Rassias stability for the Drygas functional equation<br />$$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)$$ in Banach spaces by using the Brzc{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].http://jlta.iauctb.ac.ir/article_542801_3432c898c69b45fca98bf15b68f09128.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101Linear v{C}ech closure spaces261268542813ENT. M. ChackoDepartment of Mathematics, Christian College, Chengannur-689122, Kerala, IndiaD. SushaDepartment of Mathematics, Catholicate College, Pathanamthitta-689645, Kerala, IndiaJournal Article20180209In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and product linear v{C}ech closure operators. Lastly, we describe the Moore class on the Lv{C}CS and prove that it is a vector lattice with sufficient properties.http://jlta.iauctb.ac.ir/article_542813_03b86a3d7726abe5dfb824debdc45ae9.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101A note on spectral mapping theorem269272542814ENZ. HeydarbeygiDepartment of Mathematics, Payame Noor Universtiy (PNU), P.O. BOX, 19395-4697, Tehran, IranB. MoosaviDepartment of Mathematics, Safadasht Branch, Islamic Azad University, Tehran, IranM. Shah HosseiniDepartment of Mathematics, Shahr-e-Qods Branch, Islamic Azad University, Tehran, IranJournal Article20180619This paper aims to present the well-known spectral mapping theorem for multi-variable functions.http://jlta.iauctb.ac.ir/article_542814_232ed129cf8d02dddc86184b658aa7e5.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101Algebraic distance in algebraic cone metric spaces and its properties273280545075ENK. FallahiDepartment of Mathematics, Payame Noor University, Tehran, IranG. Soleimani RadDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20180730In this paper, we prove some properties of algebraic cone metric spaces and introduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance.http://jlta.iauctb.ac.ir/article_545075_a934f93384fa651d0bf07e93cc01750b.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101On a new type of stability of a radical cubic functional equation related to Jensen mapping281292545306ENS. A. A. AL-AliDepartment of Mathematics, Faculty of Sciences, Ibn Tofail University, BP-14000, Kenitra, MoroccoY. ElkettaniDepartment of Mathematics, Faculty of Sciences, Ibn Tofail University, BP-14000, Kenitra, MoroccoJournal Article20180527The aim of this paper is to introduce and solve the radical cubic functional equation<br /> $fleft(sqrt[3]{x^{3}+y^{3}}right)+fleft(sqrt[3]{x^{3}-y^{3}}right)=2f(x)$. We also investigate some stability and hyperstability results for the considered equation in 2-Banach spaces.http://jlta.iauctb.ac.ir/article_545306_c180a4bb27125ebf0df2a7552ecd7d44.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101Digital cohomology groups of certain minimal surfaces293305545088ENI. KaracaDepartment of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey.O. EgeDepartment of Mathematics, Faculty of Science, Ege University, 35100 Izmir, Turkey.Journal Article20180806In this study, we compute simplicial cohomology groups with different coefficients of a connected sum of certain minimal simple surfaces by using the universal coefficient theorem for cohomology groups. The method used in this paper is a different way to compute digital cohomology groups of minimal simple surfaces. We also prove some theorems related to degree properties of a map on digital spheres.http://jlta.iauctb.ac.ir/article_545088_5f312172bb66e192f4dff70f2f43cb62.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201070420181101On the solving matrix equations by using the spectral representation307316545277ENA. M. NazariDepartment of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, IranS. MollaghasemiDepartment of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, IranF. BahmaniDepartment of Mathematics, Faculty of Science, Arak university, Arak, PO. Box 38156-8-8349, IranJournal Article20180603The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation. We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A, X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n times s}$ with $s < n$, which $X$ is unknown matrix. Also, we suggest the new method for solving quadratic matrix equations $AX^{2}+BX+C=0$, where $A, B, C, X in mathbb{C}^{n times n}$ and $X$ is unknown matrix with similar method.http://jlta.iauctb.ac.ir/article_545277_d043962236f83b375d3860be0b047c6d.pdf