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)Khayyam Journal of Mathematics2423-47889120230101Reviewed techniques in automatic continuity of linear functionals12916439910.22034/kjm.2022.309347.2390ENGurusamySivaDepartment of Mathematics, Alagappa University,
Karaikudi-630 004, IndiaChinnadurai GanesaMoorthyDepartment of Mathematics, Alagappa University,
Karaikudi-630 004, India0000-0003-3119-753Journal Article20211007Some techniques which were already used to derive automatic continuity results are chosen, they are modified, and extended results as well as generalized results are obtained. A technique of using the open mapping theorem and a technique of using the Hahn Banach extension theorem are explained. Results in connection with measurable cardinals are also obtained. Results for multiplicative linear functionals, positive linear functionals and uniqueness of topology are obtained. For example, sequential continuity of real multiplicative linear functionals on sequentially complete LMC algebras is obtained, when Michael's open problem is concerned only with boundedness of multiplicative linear functionals. The continuity of positive linear functionals on F-algebras with identity elements and involution is derived, when these functionals are continuous on the set of all involution-symmetric elements. Possibilities of extending the concept of positive linear functionals are considered to derive results for the continuity of such functionals on topological groups and topological vector spaces with additional structures. The technique for the Carpenter's uniqueness theorem is modified to derive boundedness of some homomorphisms. The entire article is oriented towards Michael's problem.http://www.kjm-math.org/article_164399_c0cf5d5d20930d01e1682ad575c01d48.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Anti-derivations on triangular rings303716440310.22034/kjm.2022.353067.2611ENHogerGhahramaniDepartment of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, IranMohammad NaderGhosseiriDepartment of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, IranTaherehRezaeiDepartment of Mathematics, Faculty of Science, University of Kurdistan, P.O. Box 416, Sanandaj, Kurdistan, IranJournal Article20220723The aim of this paper is to give necessary and sufficient conditions for anti-derivations to be zero on 2-torsion free triangular rings. As application of our main result, we present sufficient conditions for anti-derivations to be zero on block upper triangular matrix rings. The aim of this paper is to give necessary and sufficient conditions for anti-derivations to be zero on 2-torsion free triangular rings. As application of our main result, we present sufficient conditions for anti-derivations to be zero on block upper triangular matrix rings.http://www.kjm-math.org/article_164403_b50b645f55e6b554038865bbc80446e8.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Sharp bounds of third Hankel determinant for a class of starlike functions and a subclass of q-starlike functions385316440710.22034/kjm.2022.350982.2597ENShagunBangaDepartment of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi -110042ShanmugamSivaprasad KumarDepartment of Applied Mathematics, Delhi Technological University, Bawana Road, Rohini, Delhi -110042Journal Article20220708Following the trend of coefficient bound problems in Geometric Function Theory, in the present paper, the authors obtain the sharp bound of third Hankel determinant for the classes $S^*$, of starlike functions and $SL^*_q$, of $q$-starlike functions related with lemniscate of Bernoulli. Bound on the functions in the initial class, apart from being sharp is also an improvement over the known existing bound and the bound on the latter class generalizes the prior known outcome. Further, the extremal functions of classes $S^*$ and $SL^*_q$ are deduced to prove the sharpness of these results.http://www.kjm-math.org/article_164407_64a778d27fdececd772f105c8c7b498e.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101On strongly star semi-compactness of topological spaces546016447410.22034/kjm.2022.342863.2546ENPrasenjitBalDepartment of Mathematics, ICFAI University Tripura, Kamalghat, Tripura, INDIA-7992100000-0001-5047-7390RupamDeDepartment of Mathematics, ICFAI University Tripura, Kamalghat, Tripura, INDIA-799210Journal Article20220517Sabah et al. developed strongly star semi-compactness of a topological space in 2016, which is a variant of star-compactness in which semi-open covers are employed instead of open covers. The goal of this study is to compare the structure of strongly star semi-compactness to that of other topological characteristics with similar structures. Furthermore, the nature of a strongly star semi-compact space's subspace and the features of a strongly star semi-compact subset relative to a space are examined.http://www.kjm-math.org/article_164474_f0a9d0e5ff698c0e8f84636f26338e58.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101On φ-δ-S-primary ideals of commutative rings618016447510.22034/kjm.2022.350492.2590ENAmeerJaberDepartment of Mathematics,
Faculty of Science,
The Hashemite University,
Zarqa, JordanJournal Article20220705Let $R$ be a commutative ring with unity $(1\not=0)$ and let $\mathfrak{J}(R)$ be the set of all ideals of $R$. Let $\phi:\mathfrak{J}(R)\rightarrow\mathfrak{J}(R)\cup\{\emptyset\}$ be a reduction function of ideals of $R$ and let $\delta:\mathfrak{J}(R)\rightarrow\mathfrak{J}(R)$ be an expansion function of ideals of $R$. We recall that a proper ideal $I$ of $R$ is called a $\phi$-$\delta$-primary ideal of $R$ if whenever $a,b\in R$ and $ab\in I-\phi(I)$, then $a\in I$ or $b\in\delta(I)$. In this paper, we introduce a new class of ideals that is a generalization to the class of $\phi$-$\delta$-primary ideals. Let $S$ be a multiplicative subset of $R$ such that $1\in S$ and let $I$ be a proper ideal of $R$ with $S\cap I=\emptyset$, then $I$ is called a $\phi$-$\delta$-$S$-primary ideal of $R$ associated to $s\in S$ if whenever $a,b\in R$ and $ab\in I-\phi(I)$, then $sa\in I$ or $sb\in\delta(I)$. In this paper, we have presented a range of different examples, properties, characterizations of this new class of ideals.http://www.kjm-math.org/article_164475_83ab3afc357fe0a0d40ed82f14555b97.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Generalized derivations on Lie ideals with annihilating Engel conditions818816447610.22034/kjm.2022.351498.2600ENAshutoshPandeySchool of Liberal Studies, Ambedkar University Delhi, Delhi-110006, IndiaBalchandPrajapatiDepartment of Mathematics, Ambedkar University Delhi, Delhi-110006, IndiaJournal Article20220712Let $\mathcal{R}$ be a non-commutative prime ring with characteristic different from $2$, $\mathcal{U}$ be the Utumi quotient ring of $\mathcal{R}$ and $\mathcal{C}$ be the extended centroid of $\mathcal{R}$. Let $\mathcal{G}$ be a generalized derivation on $\mathcal{R}$, $\mathcal{L}$ be a non-central Lie ideal of $\mathcal{R}$, $0 \neq c \in\mathcal{R}$ and $ n, r, s,t$ are fixed positive integers. If $c u^s[\mathcal{G}(u^n),u^r]_ku^t =0$, for all $u \in\mathcal{L}$, then one of the following holds:
(1) $\mathcal{R}$ satisfies $s_4$.
(2) There exists $\lambda \in \mathcal{C}$ s.t. $\mathcal{G}(\zeta)= \lambda \zeta$ for all $\zeta \in \mathcal{R}$.
(3) If $\mathcal{C}$ is finite field, $\mathcal{R} \cong M_{l}(\mathcal{C})$, a $l \times l$ matrix ring over $\mathcal{C}$ for $l>2$.<br /><br />http://www.kjm-math.org/article_164476_467e23edde1750e4f8ef76ba3028ca0b.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101On matrix-valued Gabor Bessel sequences and dual frames over locally compact abelian groups8910116447810.22034/kjm.2022.354990.2625ENLalitVashishtDepartment of Mathematics, Shivaji College,
University of Delhi, Delhi-110027, IndiaUttamSinhaDepartment of Mathematics, Shivaji College,
University of Delhi, Delhi-110027, IndiaJournal Article20220805We study matrix-valued Gabor Bessel sequences and frames in the matrix-valued space $L^2(G, \mathbb{C}^{n\times n})$, where $G$ is a locally compact abelian group and $n$ is a positive integer. Firstly, we show that the Bessel condition (or upper frame condition) can be extended from $L^2(G)$ to its associated matrix-valued signal space $L^2(G,\mathbb{C}^{n\times n})$, and conversely. However, this is not true for the lower frame condition. Secondly, we give sufficient conditions for the extension of a pair of matrix-valued Bessel sequences to matrix-valued dual frames over LCA groups. A special class of matrix-valued dual generators is given. It is shown that the symmetric windows associated with a given matrix-valued Gabor frames constitutes a Gabor frame in matrix-valued spaces over LCA groups.http://www.kjm-math.org/article_164478_4b32fc06a31389c74db8589382514098.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101A study of Bessel sequences and frames via perturbations of constant multiples of the identity10211516448710.22034/kjm.2022.355505.2629ENSimaMovahedDepartment of Mathematics, Faculty of
Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, P. O. Box
98135-674, Zahedan, IranHosseinHosseini GivDepartment of Mathematics, Faculty of
Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, P. O. Box
98135-674, Zahedan, IranAlirezaAhmadi LedariDepartment of Mathematics, Faculty of
Mathematics, Statistics and Computer Science, University of Sistan and Baluchestan, P. O. Box
98135-674, Zahedan, IranJournal Article20220810We study those Bessel sequences $\{f_k\}_{k=1}^{\infty}$ in an infinite-dimensional, separable Hilbert space $H$ for which the operator $S$ defined by $Sf:=\sum_{k=1}^{\infty} \langle f,f_k\rangle f_k$ is of the form $cI+T$, for some real number $c$ and a bounded linear operator $T$, where $I$ denotes the identity operator. We use a reverse Schwarz inequality to provide conditions on $T$ and $c$ that allow $\{f_k\}_{k=1}^{\infty}$ to be a frame. Moreover, we introduce and study frames whose frame operators are compact (respectively, finite-rank) perturbations of constant multiples of the identity, frames to which we refer as compact-tight (respectively, finite-rank-tight) frames. As our final result, we prove a theorem on the weaving of certain compact-tight frames.http://www.kjm-math.org/article_164487_14305fcfe5e3748748467f9717be45eb.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101On $S$-finite conductor rings11612616448810.22034/kjm.2022.341713.2540ENAdamAnebriLaboratory of Modelling and Mathematical Structures; Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, Morocco0000-0001-5958-8548NajibMahdouLaboratory of Modelling and Mathematical Structures \\Department of Mathematics, Faculty of Science and Technology of Fez, Box 2202, University S.M. Ben Abdellah Fez, MoroccoYoussefZahirLaboratory: Mathematics, Computing and Applications- Information Security (LabMiA-SI); Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, Rabat, MoroccoJournal Article20220509Let $R$ be a commutative ring with nonzero identity and $S \subseteq R$ be a multiplicatively closed subset of $R$. In this paper, we introduce and study $S$-finite conductor rings. $R$ is said to be an $S$-finite conductor ring if $(0:a)$ and $Ra\cap Rb$ are $S$-finite ideals of $R$ for each $a,b\in R.$ Some basic properties of $S$-finite conductor rings are studied. For instance, we give necessary and sufficient conditions for a ring to be $S$-finite conductor. Also, we prove that every pre-Schreier $S$-finite conductor domain is an $S$-$GCD$ domain and the converse is true for some particular cases of $S$. Further, we examine the stability of these rings in localization and study the possible transfer to direct product, trivial ring extension and amalgamated algebra along an ideal.http://www.kjm-math.org/article_164488_4356630d77982e5912289f4bc1250d61.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Iterated function systems over arbitrary shift spaces12714316448910.22034/kjm.2022.367135.2696ENMahdiAghaeeDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, IranDawoudAhmadi DastjerdiDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University
of Guilan, Rasht, IranJournal Article20221024The orbit of a point $x\in X$ in a classical iterated function system (IFS) can be defined as $\{f_u(x)=f_{u_n}\circ\cdots \circ f_{u_1}(x):$ $u=u_1\cdots u_n$ is a word of a full shift $\Sigma$ on finite symbols and $f_{u_i}$ is a continuous self map on $X \}$. One also can associate to $\sigma=\sigma_1\sigma_2\cdots\in\Sigma$ a non-autonomous system $(X,\,f_\sigma)$ where the trajectory of $x\in X$ is defined as $x,\,f_{\sigma_1}(x),\,f_{\sigma_1\sigma_2}(x),\ldots$. Here instead of the full shift, we consider an arbitrary shift space $\Sigma$. Then we investigate basic properties related to this IFS and the associated non-autonomous systems. In particular, we look for sufficient conditions that guarantees that in a transitive IFS one may have a transitive $(X,\,f_\sigma)$ for some $\sigma\in\Sigma$ and how abundance are such $\sigma$'s.http://www.kjm-math.org/article_164489_5169ffa6f5d27c34ce7e3a585ba327b8.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Hilbert-Schmidtness of Fourier integral operators in $\mathbf{SG}$ classes14415216449010.22034/kjm.2022.351589.2601ENAbderrahmaneSenoussaouiLaboratory of Fundamental and Applied Mathematics of Oran (LMFAO),
University of Oran 1, Ahmed BEN BELLA. B.P. 1524 El M'naouar, Oran,
AlgeriaOmar FaroukAidLaboratory of Fundamental and Applied Mathematics of Oran (LMFAO),
University of Oran 1, Ahmed BEN BELLA. B.P. 1524 El M'naouar, Oran,
AlgeriaJournal Article20220713In this paper, we define a particular class of Fourier integral operators with $\mathbf{SG}$-symbol. These class of operators turn out to be bounded on the spaces $\mathcal{S}\left(\mathbb{R}^{n}\right)$ of rapidly decreasing functions and turn out to be Hilbert-Schmidt on $L^2\left(\mathbb{R}^{n}\right)$. Mainly, we prove that the Fourier integral operators with $\mathbf{SG}$-symbol are a Hilbert-Schmidt operators.http://www.kjm-math.org/article_164490_8835d5dda36598c04b28ad6138f8e5bb.pdfDepartment of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47889120230101Fully $S$-idempotent modules15316116449110.22034/kjm.2022.362523.2664ENFaranakFarshadifarDepartment of Mathematics, Farhangian University, Tehran, IranJournal Article20220917Let $R$ be a commutative ring with identity, $S$ be a multiplicatively closed subset of $R$, and $M$ be an $R$-module. A submodule $N$ of $M$ is said to be \emph{idempotent} if $N=(N:_RM)^2M$. Also, $M$ is said to be \emph{fully idempotent} if every submodule of $M$ is idempotent. The aim of this paper is to introduce the notion of fully $S$-idempotent modules as a generalization of fully idempotent modules and investigate some properties of this class of modules.http://www.kjm-math.org/article_164491_aa3a414cd8221acda43f8775017db403.pdf