2021-04-11T03:14:01Z
http://www.kjm-math.org/?_action=export&rf=summon&issue=16807
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Generalized peripherally multiplicative maps between real Lipschitz algebras with involution
Davood
Alimohammadi
Safoura
Daneshmand
Let $(X,d)$ and $(Y,\rho)$ be compact metric spaces, $\tau$ and $\eta$ be Lipschitz involutions on $ X$ and $Y$, respectively, $\mathcal{A}=Lip(X,d,\tau)$ and $\mathcal{B}=Lip(Y,\rho,\eta)$, where $Lip(X,d,\tau)=\lbrace f\in Lip(X,d):f\circ\tau=\bar{f}\rbrace $. For each $f\in \mathcal{A}$, $\sigma_{\pi,\mathcal{A}}(f)$ denotes the peripheral spectrum of $f$. We prove that if $S_{1},S_{2}:\mathcal{A}\rightarrow \mathcal{A}$ and $T_{1},T_{2}:\mathcal{A}\rightarrow \mathcal{B}$ are surjective mappings that satisfy $\sigma_{\pi,\mathcal{B}}(T_{1}(f)T_{2}(g))=\sigma_{\pi,\mathcal{A}}(S_{1}(f)S_{2}(g))$ for all $f,g\in \mathcal{A}$, then there are $\kappa_{1},\kappa_{2}\in Lip(Y,\rho,\eta)$ with $\kappa_{1}\kappa_{2}=1_{Y}$ and a Lipschitz homeomorphism $\varphi$ from $(Y,\rho)$ to $(X,d)$ with $\tau \circ\varphi=\varphi \circ \eta$ on $Y$ such that $T_{j}(f)=\kappa_{j}\cdot(S_{j}(f)\circ\varphi)$ for all $f\in \mathcal{A}$ and $j=1,2$. Moreover, we show that the same result holds for surjective mappings $S_{1},S_{2}:\mathcal{A}\rightarrow \mathcal{A}$ and $T_{1},T_{2}:\mathcal{A}\rightarrow \mathcal{B}$ that satisfy $\sigma_{\pi,\mathcal{B}}(T_{1}(f)T_{2}(g))\cap\sigma_{\pi,\mathcal{A}}(S_{1}(f)S_{2}(g))\neq\emptyset$ for all $f,g\in \mathcal{A}$.
Peripheral spectrum
norm multiplicative
peaking function
$(i)$-peaking function
weighted composition operator
2021
01
01
1
31
http://www.kjm-math.org/article_123046_39ebcb541a05a639e530b9a5a3a5fc0e.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
A cartesian closed subcategory of topological molecular lattices
Ghasem
Mirhosseinkhani
Mahboobeh
Akbarpour
A category C is called cartesian closed provided that it has ﬁnite products and for each C-object A the functor (A×−) : A → A has a right adjoint. It is well known that the category TML of topological molecular lattices with generalized order homomorphims in the sense of Wang is both complete and cocomplete, but it is not cartesian closed. In this paper, we introduce a cartesian closed subcategory of this category.
Topological molecular lattices
Exponentiable object
Cartesian closed category
2021
01
01
32
39
http://www.kjm-math.org/article_123047_ba83a4356cfaf58601dadafd004634b7.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Almost and weakly NSR, NSM and NSH spaces
Ljubisa
Kocinac
Rachid
Lakehal
Djamila
Seba
In this paper we introduce and study some new types of star-selection principles (almost and weakly neighbourhood star-Menger, neighbourhood star-Rothberger and neighbourhood star-Hurewicz). We establish some properties of these selection principles and their relations with other selection properties of topological spaces. Behaviour of these classes of spaces under certain kinds of mappings is also considered.
Selection principles
star-Menger
star-Rothberger
almost NSM
weakly NSM
2021
01
01
40
51
http://www.kjm-math.org/article_123048_64af716d7e2165b79e543fdc6760fe3a.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Numerical simulation for a class of singularly perturbed convection delay problems
Murali Mohan Kumar
Palli
A.S.V.
Ravi Kanth
This article presents a solution for a class of singularly perturbed convection with delay problems arising in control theory. The approach of extending Taylor's series for the convection term gives to a bad approximation when the delay is not smaller order of singular perturbation parameter. To handle the delay term, we model an interesting mesh form such that the delay term lies on mesh points. The parametric cubic spline is adapted to the continuous problem on a specially designed mesh. The truncation error for the proposed method is derived. Numerical examples are experimented to examine the effect of the delay parameter on the layer structure.
Parametric cubic spline
Singular perturbation
Oscillatory
2021
01
01
52
64
http://www.kjm-math.org/article_123049_f09f8c2bf11cfffa3f1889fb0187a397.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
On $Smathcal{I}H$-property and $SSmathcal{I}H$-property in topological spaces
Manoj
Bhardwaj
Brij Kishore
Tyagi
Sumit
Singh
In this paper, we further investigated the $SS \mathcal{I} H$ and $S \mathcal{I} H$ properties introduced by Das et. al recently. It is shown that regular-closed $G_\delta$ subspace of $SS \mathcal{I} H$ (resp., $S \mathcal{I} H$) is not $SS \mathcal{I} H$ (resp., $S \mathcal{I} H$). The preservation properties of these spaces are studied under some maps. Also $SS \mathcal{I} H$ and $S \mathcal{I} H$ properties are investigated in Alexandroff space.
Hurewicz space
Stone-$acute{C}$ech compactification
strongly star-$mathcal{I}$-Hurewicz
star-$mathcal{I}$-Hurewicz property
2021
01
01
65
76
http://www.kjm-math.org/article_123050_260ec1358e9cecfff939e2bfde28a389.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Topological characterization of chainable sets and chainability via continuous functions
Gholam Reza
Rezaei
Mohammad Sina
Asadzadeh
Javad
Jamalzadeh
In the last decade, the notions of function-f-ϵ-chainability, uniformly function-f-ϵ-chainability, function-f-ϵ-chainable sets and locally functionf-chainable sets were studied in some papers. We show that the notions of function-f-ϵ-chainability and uniformly function-f-ϵ-chainability are equivalent to the notion of non-ultrapseudocompactness in topological spaces. Also, all of these are equivalent to the condition that each pair of non-empty subsets (resp., subsets with non-empty interiors) is function-f-ϵ-chainable (resp., locally function-f-chainable). Further, we provide a criterion for connectedness with covers. In the paper "Characterization of ϵ-chainable sets in metric spaces" (Indian J. Pure Appl. Math. 33 (2002), no. 6, 933{940), the chainability of a pair of subsets in a metric space has been defined wrongly and consequently Theorem 1 and Theorem 5 are found to be wrong. We rectify their definition appropriately and consequently, we give appropriate results and counterexamples.
ϵ-chainable
function-f-chainable
ultrapseudocompact
2021
01
01
77
85
http://www.kjm-math.org/article_123052_e4c5804fe16f5bd6826091dbe093035d.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
A note on quasilinear parabolic systems in generalized spaces
Elhoussine
Azroul
Farah
Balaadich
We study the existence of solutions for quasilinear parabolic systems of the form \[\partial_tu-\text{div}\,\sigma(x,t,Du)=f\quad\text{in}\;Q=\Omega\times(0,T),\] whose right hand side belongs to $W^{-1,x}L_{\overline{M}}(Q;\R^m)$, supplemented with the conditions $u=0$ on $\partial\Omega\times(0,T)$ and $u(x,0)=u_0(x)$ in $\Omega$. By using a mild monotonicity condition for $\sigma$, namely strict quasimonotone, and the theory of Young measures, we deduce the needed result.
Quasilinear parabolic systems
Orlicz-Sobolev spaces
Young measures
2021
01
01
86
95
http://www.kjm-math.org/article_123053_c7a14ce25359e34125f6f9f0a926b6b2.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Some numerical radius inequalities for the v{C}ebyv{s}ev functional and non-commutative Hilbert space operators
Mohammad
Alomari
In this work, a Gruss inequality for positive Hilbert space operators is proved. So, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound for the numerical radius of the summand of two bounded linear Hilbert space operators is proved. A commutative version is also obtained as well.
Cebysev functional
Numerical radius
non-commutative operators
2021
01
01
96
108
http://www.kjm-math.org/article_123054_95180e8fafd8455d3b205a32b33c39df.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Maps strongly preserving the square zero of $ lambda $-Lie product of operators
Roja
Hosseinzadeh
Let $\mathcal{A}$ be a standard operator algebra on a Banach space $\mathcal{X}$ with $\dim \mathcal{X}\geq 2$. In this paper, we characterize the forms of additive maps on $\mathcal{A}$ which strongly preserve the square zero of $ \lambda $-Lie product of operators, i.e., if $\phi:\mathcal{A}\longrightarrow \mathcal{A}$ is an additive map which satisfies $$ [A,B]^2_{\lambda}=0 \Rightarrow [\phi(A),B]^2_{\lambda}=0,$$ for every $A,B \in \mathcal{A}$ and for a scalar number $\lambda$ with $\lambda \neq -1$, then it is shown that there exists a function $\sigma: \mathcal{A} \rightarrow \mathbb{C}$ such that $\phi(A)= \sigma(A) A$, for every $A \in \mathcal{A}$.
Preserver problem
Standard operator algebra
$ lambda $-Lie product
Lie product
2021
01
01
109
114
http://www.kjm-math.org/article_123055_e133eab51da403a9932eca15e4692c88.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Some remarks on chaos in nonautonomous dynamical systems
Ali Reza
Zamani Bahabadi
Mona
Effati
Bahman
Honary
We introduce the concept of almost thick chaos and continuously almost thick transitivity for continuous maps and nonautonomous dynamical systems (NDS). We show that NDS $f_{1,\infty}$ is sensitive if it is thick transitive and syndetic. Under certain conditions, we show that NDS $(X,f_{1,\infty})$ generated by a sequence $(f_n)$ of continuous maps on $X$ converging uniformly to $f$ is almost thick transitive if and only if $(X,f)$ is almost thick transitive. Moreover, we prove that if $f_{1,\infty}$ is continuously almost thick transitive and syndetic, then it is strongly topologically ergodic. In addition, the relationship between the large deviations theorem and almost thick chaos is studied.
Nonautonomous dynamical systems
Transitivity
Sen- sitivity
chaos
2021
01
01
115
130
http://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Algorithm for computing a common solution of equilibrium and fixed point problems with set-valued demicontractive operators
Thierno
Sow
In this paper, we introduce an iterative algorithm based on the well-known Krasnoselskii-Mann's method for finding a common element of the set of fixed points of multivalued demicontractive mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved without imposing any compactness condition on the mapping or the space. We further applied our results to solve some optimization problems. Our results improve many recent results using Krasnoselskii-Mann's algorithm for solving nonlinear problems.
Explicit algorithm
Set-valued operators
Equilibrium problems
Fixed points problems
2021
01
01
131
139
http://www.kjm-math.org/article_123057_4862cd9ff26a4cf82d42841c7c89291d.pdf
Khayyam Journal of Mathematics
Khayyam J. Math.
2021
7
1
Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces
Mohamed
Bourahma
Abdelmoujib
Benkirane
Jaouad
Bennouna
In this study, we prove an existence result of renormalized solutions for nonlinear parabolic equations of the type $$ \displaystyle\frac{\partial b(x,u)}{\partial t} -\mbox{div}\>a(x,t,u,\nabla u)-\mbox{div}\> \Phi(x,t,u)= f \quad\mbox{in }{Q_T=\Omega\times (0,T)}, $$ where $b(x,\cdot)$ is a strictly increasing $C^1$-function for every $x\in\Omega$ with $b(x,0)=0$, the lower order term $\Phi$ satisfies a natural growth condition described by the appropriate Orlicz function $M$ and $f$ is an element of $L^1(Q_T)$. We don't assume any restriction neither on $M$ nor on its conjugate $\overline{M}$.
Parabolic problem
Orlicz spaces
Renormalized solutions
Generalized growth
2021
01
01
140
164
http://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf