Khayyam Journal of Mathematics
https://www.kjm-math.org/
Khayyam Journal of Mathematicsendaily1Sat, 01 Jul 2023 00:00:00 +0430Sat, 01 Jul 2023 00:00:00 +0430Inclusions and coincidences for multiple Cohen positive strongly $p$−summing $m$−linear operators
https://www.kjm-math.org/article_182689.html
In this paper we compare the new class of multiple Cohen positive strongly $p$-summing multilinear operators along with different classes of positive multilinear summability including the classes of Cohen positive strongly summing $m$-linear operators and positive multiple summing $m$-linear operators. Moreover, we investigate a duality relationship in terms of tensor norm.A note on an algorithm for solution of the Lyapunov matrix equation
https://www.kjm-math.org/article_182692.html
In this paper, a matrix iterative algorithm is resorted to in the aim to solve numerically the well-known Lyapunov matrix equation $AX+XA^T=C$ that arises in some areas of applied science. Some numerical examples illustrating the significance of our approach and showing the interest of this work are provided as well.Selection games with minimal usco maps
https://www.kjm-math.org/article_182713.html
We establish relationships between various topological selection games involving the space of minimal usco maps with various topologies, including the topology of pointwise convergence and the topology of uniform convergence on compact sets, and the underlying domain using full- and limited-information strategies. We also tie these relationships to analogous results related to spaces of continuous functions. The primary games we consider include Rothberger-like games, generalized point-open games, strong fan-tightness games, Tkachuk's closed discrete selection game, and Gruenhage's \(W\)-games.General energy decay for a viscoelastic wave equation with space-time damping coefficient in $\mathbb{R}^n$
https://www.kjm-math.org/article_182714.html
In this paper, we consider the following viscoelastic wave equation \begin{equation}\small\nonumber\left\{\begin{split}&amp;u_{tt} -\bigl(\Delta u-\int^t_0 g(t-s)\Delta u(s) ds\bigr) + b(t , x) u_t +|u|^{p-1} u =0,\quad t &gt;0, \; x\in \mathbb{R}^n\\&amp;u(0 , x ) = u_0(x), \qquad u_t(0 , x) = u_1(x), \qquad x\in \mathbb{R}^n,\end{split}\right.\end{equation}with space-time dependent potential and where the initial data $u_0(x)$, $u_1(x)$ have compact supports. Under suitable assumptions on the potential $b$ and for a relaxation function $g$ satisfying the condition $g^{\prime}(t) \leq -\mu(t) g^r(t),\quad t\geq 0,\; 1&lt; r&lt;\frac{3}{2}$, we obtain a general energy decay result that extends other results in the literature.On better approximation order for the nonlinear Bleimann-Butzer-Hahn operator of maximum product kind
https://www.kjm-math.org/article_182720.html
Using maximum instead of sum, nonlinear Bleimann-Butzer-Hahn operator of maximum product kind was introduced. The present paper deals with the approximation processes for this operator. In a previous study, it was indicated that the order of approximation of this operator to the function f under the modulus is $((x+1)^{(3/2)}&radic;x)/(&radic;n)$ and it could not be improved except for some subclasses of functions. Contrary to this claim, under some special conditions, we will show that a better order of approximation can be obtained with the help of classical and weighted modulus of continuities.Lie ideals and generalized derivations in prime rings and Banach algebras
https://www.kjm-math.org/article_182723.html
Let $R$ be a prime ring and $L$ a non-central Lie ideal of $R$. The main purpose of this paper is to describe generalized derivations of $R$ satisfying some algebraic identities on $L$. Moreover, using a topological approach based on Baire&rsquo;s category theorem and some properties of functional analysis, our results have been extended to Banach algebras.On the Betti numbers of monomial ideals and their powers
https://www.kjm-math.org/article_182724.html
Let $S=\mathbb K[x_1,\ldots,x_n]$ the polynomial ring over a field $\mathbb K$. In this paper for some families of monomial ideals $I \subset S$ we study the minimal number of generators of $I^k$. We use this results to find some other Betti numbers of these families of ideals for special choices of $n$, the number of variables.Boundedness of the Hardy-Littlewood maximal operator, fractional integral operators, and Calder\'on-Zygmund operators on generalized weighted Morrey spaces
https://www.kjm-math.org/article_182725.html
In this paper we investigate the boundedness of three classical operators, namely the Hardy-Littlewood maximal operator, fractional integral operators, and Calder\'{o}n-Zygmund operators, on generalized weighted Morrey spaces and generalized weighted weak Morrey spaces. We prove that each of the three operators is bounded on these function spaces under some assumptions.Applications of nonhomogenous Cauchy-Euler fractional $q$-differential equation to a new class of analytic functions
https://www.kjm-math.org/article_182726.html
In this paper, we define a new general fractional $q$-differential operator and by means of this operator we introduce a new subclass of analytic functions which are the solutions of the nonhomogenous Cauchy-Euler fractional $q$-differential equations. Our aim is to determine upper bounds of Taylor-Maclaurin coefficients for functions belong to this class.Subordination problems for certain meromorphic functions
https://www.kjm-math.org/article_182727.html
Let $\Sigma$ be the class of meromorphic functions $f(z)$ of the form $f(z)=\frac{1}{z}+a_0+a_1z+\cdots$ which are analytic in the punctured disk $\mathbb{U}_0.$ For $f(z)\in\Sigma,$ operators $D^n f(z)$ with $n\in \mathbb{Z}=\{\cdots,-1,0,1,\cdots\}$ are introduced. Applying differential subordinations for analytic functions in the open unit disc $\mathbb{U},$ some interesting properties of $f(z)\in\Sigma$ with $D^n f(z)$ are discussed and argument problems of $D^n f(z)$ are given. Also, we consider some simple problems for our results.Conformally closed weakly Berwald metrics
https://www.kjm-math.org/article_182728.html
A weakly Berwald metric is called a conformally closed weakly Berwald metric if for any conformal change remains a weakly Berwald metric. In this paper, we study the conformally closed weakly Berwald metrics and find the necessary and sufficient condition under which a weakly Berwald metric be conformally closed. We show that a Randers metric is a conformally closed weakly Berwald metric if and only if it is a Riemannian metric or the conformal transformation is homothety.Some cohomological properties of generalized module extension Banach algebras
https://www.kjm-math.org/article_182729.html
Let $A$ and $X$ be Banach algebras such that $X$ is a Banach algebraic $A$-module. The generalized module extension $A\bowtie X$, which is a strongly splitting Banach algebra extension of $X$ by $A$, was recently introduced and studied. Many known Banach algebras such as module extension, Lau product, (generalized) semidirect product and also the direct product of Banach algebras have this general framework. We first investigate the $n$-weak amenability of $A\bowtie X$ and then we characterize its cyclic amenability improving some known results. We also examine our results to some special generalized module extension algebras. Furthermore, we characterize the cyclic amenability of some concrete Banach algebras related to locally compact groups.