Sahand Communications in Mathematical Analysis
https://scma.maragheh.ac.ir/
Sahand Communications in Mathematical Analysisendaily1Mon, 01 Feb 2021 00:00:00 +0330Mon, 01 Feb 2021 00:00:00 +0330Some Properties of Lebesgue Fuzzy Metric Spaces
https://scma.maragheh.ac.ir/article_46667.html
In this paper, we establish a sequential characterisation of Lebesgue fuzzy metric and explore the relationship between Lebesgue, weak $G$-complete and compact fuzzy metric spaces. We also discuss the Lebesgue property of several well-known fuzzy metric spaces.A Note on Some Results for $C$-controlled $K$-Fusion Frames in Hilbert Spaces
https://scma.maragheh.ac.ir/article_46575.html
In this manuscript, we study the relation between K-fusion frame and its local components which leads to the definition of a $C$-controlled $K$-fusion frames, also we extend a theory based on K-fusion frames on Hilbert spaces, which prepares exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we define the analysis, synthesis and frame operator for $C$-controlled $K$-fusion frames, which even yield a reconstruction formula. Also, we define dual of $C$-controlled $K$-fusion frames and study some basic properties and perturbation of them.On Approximation of Some Mixed Functional Equations
https://scma.maragheh.ac.ir/article_46665.html
In this paper,&nbsp; we have improved some of the results in [C. Choi and&nbsp;&nbsp; B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional Equations. Results Math.&nbsp; 75&nbsp; no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following&nbsp;&nbsp; functional equations\begin{align*}&nbsp; 2\varphi(x + y) + \varphi(x - y) &amp;= 3\varphi(x)+ 3\varphi(y)&nbsp; \\&nbsp; 2\psi(x + y) + \psi(x - y) &amp;= 3\psi(x) + 2\psi(y) + \psi(-y).\end{align*}We also consider the Pexider type functional equation \[2\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive functional equation\[2\psi(x + y) + \psi(x - y) = 3\psi(x) + \psi(y).\]Gabor Dual Frames with Characteristic Function Window
https://scma.maragheh.ac.ir/article_46666.html
The duals of Gabor frames have an essential role in reconstruction of signals. In this paper we find a necessary and sufficient&nbsp; condition for two Gabor systems $\left(\chi_{\left[c_1,d_1\right)},a,b\right)$ and $\left(\chi_{\left[c_2,d_2\right)},a,b\right)$ to form dual frames for $L_2\left(\mathbb{R}\right)$, where $a$ and $b$ are positive numbers and $c_1,c_2,d_1$ and $d_2$ are real numbers such that $c_1&lt;d_1$ and $c_2&lt;d_2$.$K$-orthonormal and $K$-Riesz Bases
https://scma.maragheh.ac.ir/article_47114.html
Let $K$ be a bounded operator. $K$-frames are ordinary frames for the range $K$. These frames are a generalization of ordinary frames and are certainly different from these frames. This research introduces a new concept of bases for the range $K$. Here we define the&nbsp; $K$-orthonormal basis and the $K$-Riesz basis, and then we describe their properties. As might be expected, the $K$-bases differ from the ordinary ones mentioned in this article.On New Extensions of Hermite-Hadamard Inequalities for Generalized Fractional Integrals
https://scma.maragheh.ac.ir/article_239415.html
In this paper, we establish some Trapezoid and Midpoint type inequalities for generalized fractional integrals by utilizing the functions whose second derivatives are bounded . We also give some new inequalities for $k$-Riemann-Liouville fractional integrals as special cases of our main results. We also obtain some Hermite-Hadamard type inequalities by using the condition $f^{\prime }(a+b-x)\geq f^{\prime }(x)$ for all $x\in \left[ a,\frac{a+b}{2}\right] $ instead of convexity.Some bi-Hamiltonian Systems and their Separation of Variables on 4-dimensional Real Lie Groups
https://scma.maragheh.ac.ir/article_239419.html
In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix&nbsp; for this family of bi-Hamiltonian structures, we obtain an explicit process for finding&nbsp; the variables of separation and the separated relations in detail.A Fixed Point Theorem for Weakly Contractive Mappings
https://scma.maragheh.ac.ir/article_240244.html
In this paper, we generalize the concepts of weakly Kannan, weakly Chatterjea and weakly Zamfirescu for fuzzy metric spaces. Also, we investigate Banach's fixed point theorem for the mentioned classes of functions in these spaces. Moreover, we show that the class of weakly Kannan and weakly Chatterjea maps are subclasses of the class of weakly Zamfirescu maps.On Some Coupled Fixed Point Theorems with Rational Expressions in Partially Ordered Metric Spaces
https://scma.maragheh.ac.ir/article_240245.html
The aim of this paper is to prove some coupled fixed point&nbsp; theorems of&nbsp; a self mapping satisfying a certain rational type contraction along with&nbsp; strict mixed monotone property in an ordered metric space. Further, a result&nbsp; is presented for the uniqueness of a coupled fixed point under an order relation in a space. These results generalize and extend known existing results in the literature.Joint Continuity of Bi-multiplicative Functionals
https://scma.maragheh.ac.ir/article_240861.html
For Banach algebras $\mathcal{A}$ and $\mathcal{B}$, we show that if $\mathfrak{A}=\mathcal{A}\times \mathcal{B}$ is unital, then each bi-multiplicative mapping from $\mathfrak{A}$ into a semisimple commutative Banach algebra $\mathcal{D}$ is jointly continuous. This conclusion generalizes&nbsp; a famous result due to$\check{\text{S}}$ilov, concerning the automatic continuity of homomorphisms between Banach algebras. We also prove that every $n$-bi-multiplicative functionals on $\mathfrak{A}$ is continuous if and only if it is continuous for the case $n=2$.&nbsp;Fixed Point Theorems for Geraghty Type Contraction Mappings in Complete Partial $b_{v}\left( s\right) $-Metric Spaces
https://scma.maragheh.ac.ir/article_242300.html
In this paper, necessary and sufficient conditions for the existence and uniqueness of fixed points of generalized Geraghty type contraction mappings are given in complete partial $b_{v}(s) $-metric spaces. The results are more general than several results that exist in the literature because of the considered space. A numerical example is given to support the obtained results. Also, the existence and uniqueness of the solutions of an integral equation has been verified considered as an application.Some Properties of Complete Boolean Algebras
https://scma.maragheh.ac.ir/article_242304.html
The main result of this paper is a characterization of the strongly algebraically closed algebras in the&nbsp; lattice of all real-valued continuous functions and the equivalence classes of $\lambda$-measurable. We shall provide conditions&nbsp; which strongly algebraically closed algebras carry a strictly positive Maharam submeasure. Particularly, it is proved that if $B$ is a strongly algebraically closed lattice&nbsp; and $(B,\, \sigma)$ is a Hausdorff space&nbsp; and $B$ satisfies&nbsp; the&nbsp;&nbsp; $G_\sigma$ property, then $B$ carries a strictly positive Maharam submeasure.Second Module Cohomology Group of Induced Semigroup Algebras
https://scma.maragheh.ac.ir/article_242308.html
For a discrete semigroup $ S $ and a left multiplier operator&nbsp; $T$ on&nbsp; $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective,&nbsp; then the second module cohomology groups $\mathcal{H}_{\ell^1(E)}^{2}(\ell^1(S), \ell^{\infty}(S))$ and $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1({S_{T}}), \ell^{\infty}(S_{T}))$ are equal, where $E$ and&nbsp; $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$,&nbsp;&nbsp; respectively.&nbsp; Finally, we show thet, for every odd $n\in\mathbb{N}$,&nbsp; $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1(S_{T}),\ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.Two Equal Range Operators on Hilbert $C^*$-modules
https://scma.maragheh.ac.ir/article_242934.html
In this paper, number of properties, involving invertibility, existence of Moore-Penrose inverse and etc for modular operators with the same ranges on Hilbert $C^*$-modules&nbsp; are presented. Natural decompositions of operators with closed range enable us to find some relations of the product of operators with&nbsp; Moore-Penrose inverses under the condition that they have&nbsp; the same ranges&nbsp; in Hilbert $C^*$-modules. The triple reverse order law and the mixed reverse order law in the special cases are also given. Moreover, the range property and Moore-Penrose inverse are illustrated.