Generalized peripherally multiplicative maps between real Lipschitz algebras with involution
Davood
Alimohammadi
Department of Mathematics, Faculty of Science, Arak University
author
Safoura
Daneshmand
Department of Mathematics, Faculty of Science, Arak University
author
text
article
2021
eng
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 $f,g\in \mathcal{A}$.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
1
31
http://www.kjm-math.org/article_123046_39ebcb541a05a639e530b9a5a3a5fc0e.pdf
dx.doi.org/10.22034/kjm.2020.200073.1555
A cartesian closed subcategory of topological molecular lattices
Ghasem
Mirhosseinkhani
Department of Mathematics, Sirjan University of technology
author
Mahboobeh
Akbarpour
Department of Mathematics, University of Hormozgan, Bandarabbas, Iran
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
32
39
http://www.kjm-math.org/article_123047_ba83a4356cfaf58601dadafd004634b7.pdf
dx.doi.org/10.22034/kjm.2020.117858.1095
Almost and weakly NSR, NSM and NSH spaces
Ljubisa
Kocinac
Department of Mathematics, Faculty of Sciences and Mathematics, University of Nis, Nis, Serbia
author
Rachid
Lakehal
Dynamic of Engines and Vibroacoustic Laboratory,
University M'Hamed Bougara of Boumerdes, Algeria
author
Djamila
Seba
Dynamic of Engines and Vibroacoustic Laboratory,
University M'Hamed Bougara of Boumerdes, Algeria
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
40
51
http://www.kjm-math.org/article_123048_64af716d7e2165b79e543fdc6760fe3a.pdf
dx.doi.org/10.22034/kjm.2020.224608.1753
Numerical simulation for a class of singularly perturbed convection delay problems
Murali Mohan Kumar
Palli
GMR Institute of Technology
author
A.S.V.
Ravi Kanth
Department of Mathematics
National Institute of Technology, Kurukshetra
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
52
64
http://www.kjm-math.org/article_123049_f09f8c2bf11cfffa3f1889fb0187a397.pdf
dx.doi.org/10.22034/kjm.2020.210616.1650
On $S\mathcal{I}H$-property and $SS\mathcal{I}H$-property in topological spaces
Manoj
Bhardwaj
University of Delhi, India
author
Brij Kishore
Tyagi
A.R.S.D. College, University of Delhi, India
author
Sumit
Singh
University of Delhi, India
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
65
76
http://www.kjm-math.org/article_123050_260ec1358e9cecfff939e2bfde28a389.pdf
dx.doi.org/10.22034/kjm.2020.209741.1637
Topological characterization of chainable sets and chainability via continuous functions
Gholam Reza
Rezaei
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
author
Mohammad Sina
Asadzadeh
Department of Mathematics, University of Sistan and Baluchestan, Zahedan,
Iran.
author
Javad
Jamalzadeh
Department of Mathematics, University of Sistan and Baluchestan, Zahedan,
Iran.
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
77
85
http://www.kjm-math.org/article_123052_e4c5804fe16f5bd6826091dbe093035d.pdf
dx.doi.org/10.22034/kjm.2020.219320.1710
A note on quasilinear parabolic systems in generalized spaces
Elhoussine
Azroul
Department of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ
author
Farah
Balaadich
Departement of Mathematics, Faculty of Sciences, Dhar El Mahraz FEZ
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
86
95
http://www.kjm-math.org/article_123053_c7a14ce25359e34125f6f9f0a926b6b2.pdf
dx.doi.org/10.22034/kjm.2020.211591.1660
Some numerical radius inequalities for the \v{C}eby\v{s}ev functional and non-commutative Hilbert space operators
Mohammad
Alomari
Jadara University,
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
96
108
http://www.kjm-math.org/article_123054_95180e8fafd8455d3b205a32b33c39df.pdf
dx.doi.org/10.22034/kjm.2020.205545.1598
Maps strongly preserving the square zero of $ \lambda $-Lie product of operators
Roja
Hosseinzadeh
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.
author
text
article
2021
eng
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 $A \in \mathcal{A}$.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
109
114
http://www.kjm-math.org/article_123055_e133eab51da403a9932eca15e4692c88.pdf
dx.doi.org/10.22034/kjm.2020.210055.1640
Some remarks on chaos in nonautonomous dynamical systems
Ali Reza
Zamani Bahabadi
Ferdowsi University of Mashhad
author
Mona
Effati
Pure Mathematics, Faculty of Mathematical science, Mashhad, Iran
author
Bahman
Honary
Ferdowsi university of Mashhhad
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
115
130
http://www.kjm-math.org/article_123056_08214b4428e55ce385d320df099089aa.pdf
dx.doi.org/10.22034/kjm.2020.209183.1631
Algorithm for computing a common solution of equilibrium and fixed point problems with set-valued demicontractive operators
Thierno
Sow
Gaston Berger university
author
text
article
2021
eng
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.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
131
139
http://www.kjm-math.org/article_123057_4862cd9ff26a4cf82d42841c7c89291d.pdf
dx.doi.org/10.22034/kjm.2020.208829.1623
Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces
Mohamed
Bourahma
Laboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez Morocco
author
Abdelmoujib
Benkirane
Laboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez Morocco
author
Jaouad
Bennouna
Laboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez Morocco
author
text
article
2021
eng
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 $\overline{M}$.
Khayyam Journal of Mathematics
Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)
2423-4788
7
v.
1
no.
2021
140
164
http://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf
dx.doi.org/10.22034/kjm.2020.184027.1422