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 Mathematics2423-47888220220701Almost separable spaces12012715465610.22034/kjm.2022.267072.2136ENSagarmoyBagBangabasi Evening College, 19 Rajkumar Chakraborty Sarani, Kolkata-700009, West Bengal, IndiaRam ChandraMannaRamakrishna Mission Vidyamandir, Belur Math, Howrah-711202, West Bengal, IndiaSourav KantiPatraDepartment of Pure and Applied Science, Midnapore City College, Kuturia, Bhadutala-721129, West Bengal, IndiaJournal Article20210112In this article, we introduce the notion of almost separable space, which is a generalization of separable space. We show that like separability, almost separability is $c$-productive and the converse is true under some restrictions. We discuss about the cardinality of the set of all real valued continuous functions on an almost separable space. Finally, we establish a Baire Category Like theorem on pseudocompact space.http://www.kjm-math.org/article_154656_dcb70dbdd76858538e6237ced4a74464.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 Mathematics2423-47888220220701Oscillations of higher-order impulsive partial differential equations with distributed delay12814215465710.22034/kjm.2022.295254.2324ENYasarBolatDepartment of Mathematics, Kastamonu University, Turkey.George EChatzarakisDepartment of Electrical and Electronic Engineering
Educators, School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens, GreeceSpiros LPanetsosDepartment of Electrical and Electronic Engineering
Educators, School of Pedagogical and Technological Education (ASPETE),
Marousi 15122, Athens, GreeceT.RajaDepartment of Mathematics, Mahendra College of Engineering,
(Affiliated to Anna University, Chennai), Salem (Dt), Tamil Nadu, India0000-0002-1829-1729Journal Article20210715In this paper, we will consider a class of boundary value problems associated with even order nonlinear impulsive neutral partial functional differential equations with continuous distributed deviating arguments and damping term. Necessary and sufficient conditions are obtained for the oscillation of all solutions using impulsive differential inequalities and integral averaging scheme with the Robin boundary condition. Examples illustrating the results are also given.http://www.kjm-math.org/article_154657_817fbcb4eeca3647824aa765c56d9838.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 Mathematics2423-47888220220701Uncertainty principles on nilpotent Lie groups14316215467810.22034/kjm.2022.305501.2374ENAjayKumarDepartment of Mathematics, University of Delhi, Delhi, 110007, IndiaJyotiSharmaDepartment of Mathematics, Daulat Ram College, University of Delhi, Delhi, 110007, IndiaJournal Article20210918We prove Hardy’s type uncertainty principle on connected nilpotent Lie groups for the Fourier transform is proved. An analogue of Hardy’s theorem for Gabor transform has been established for connected and simply connected nilpotent Lie groups . Finally Beurling’s theorem for Gabor transform is discussed for groups of the form R^n × K, where K is a compact group.http://www.kjm-math.org/article_154678_543eb0018bddc013db0529ee7562aded.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 Mathematics2423-47888220220701When nilpotence implies the zeroness of linear operators16317315468010.22034/kjm.2022.244524.1972ENNassimaFridDepartment de
Mathematiques, "Universit\'{e} Oran 1, Ahmed Ben Bella, B.P. 1524, El
Menouar, Oran 31000, AlgeriaMohammed HichemMortadDepartment de
Mathematiques, "Universit\'{e} Oran 1, Ahmed Ben Bella, B.P. 1524, El
Menouar, Oran 31000, AlgeriaSouheybDehimiDepartment of Mathematics, Faculty of Mathematics and Informatics,
University of Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj,
El-Anasser 34030, AlgeriaJournal Article20200819In this paper, we give conditions forcing nilpotent operators (everywhere defined and bounded or closed) to be null. More precisely, it is mainly shown any closed or everywhere defined bounded nilpotent operator with a positive (self-adjoint) real part is automatically null. Some other interesting examples and results accompagny our results.http://www.kjm-math.org/article_154680_cd48eb208ffadc9307a8165f018a5e97.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 Mathematics2423-47888220220701Description of $J$-sets and $C$-sets by matrices17417715468410.22034/kjm.2022.295836.2328ENHediehHosseiniDepartment of Mathematics, Faculty of Sciences, Shahed UniversityMohammadAkbari TootkaboniDepartment of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan0000-0002-4183-8817Journal Article20210719 We redefine the notion of $J$-sets in a commutative semigroup $S$ with the help of matrices whose entries are functions from the natural numbers into $S$. We show that our definition of $J$-sets is equivalent to the standard definition of $J$-sets. We also introduce a new notion of $C$-set using matrices whose entries are functions from the natural numbers into $S$.http://www.kjm-math.org/article_154684_6a79c01fbe2a885221a21cc11a5897a5.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 Mathematics2423-47888220220701A nonmonotonic explicit proximal-like method for solving equilibrium programming with convex constraints17819415468610.22034/kjm.2022.263701.2113ENNopparatWairojjanaApplied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage, Pathumthani 13180, Thailand.NuttapolPakkaranangMathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand.0000-0002-0224-4661KanikarMuangchooFaculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand.0000-0003-0975-2623NattawutPholasaSchool of Science, University of Phayao, Phayao, 56000, Thailand.Journal Article20201225In this paper, we propose a new proximal-type method to solve equilibrium problems in a real Hilbert space. The new method is analogous to the famous two step extragradient method that is used to solve variational inequalities in the Hilbert spaces. The proposed iterative scheme uses a new non-monotone step size rule based on local bifunction information instead of any line search method. A strong convergence theorem for the proposed method is well-established by taking mild conditions on a bifunction. The applications of the main results to solve fixed point problems and variational inequalities are presented. Finally, we examined two test problems for computational experiments and demonstrated the validity and effectiveness of the proposed method.http://www.kjm-math.org/article_154686_8baf9385426e69b8a4595a9530a41d5f.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 Mathematics2423-47888220220701Matrix summability of sequences of sets19520315468710.22034/kjm.2022.327963.2476ENFatihNurayDepartment of Mathematics, Afyon Kocatepe University, Afyonkarahisar, TurkeyJournal Article20220203In this paper the definition of strong Cesaro summability of sequences of closed sets with respect to a modulus is extended to a definition of strong $T$-summability with respect to a modulus when $T$ is a nonnegative regular matrix summability method. Also, we show that if a sequence of closed sets is strongly $T$-summable with respect to an arbitrary modulus, then it is $T$-statistically convergent and that $T$-statistical convergence and strong $T$-summability with respect to a modulus are equivalent on the bounded sequences of closed sets.http://www.kjm-math.org/article_154687_1ad512502ad8fa8cd3f7d3be443b1542.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 Mathematics2423-47888220220701Richardson extrapolation of Kantorovich and degenerate kernel methods for Fredholm integral equations of the second kind20421815468810.22034/kjm.2022.336277.2513ENChafikAllouchUniversity Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, MoroccoMohamedArraiUniversity Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, MoroccoHamzaBoudaUniversity Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, MoroccoJournal Article20220406In this paper, we propose two methods based on projections for approximating the solution of Fredholm integral equations of the second kind. The projection is either the orthogonal projection or an interpolatory projection onto a space of piecewise polynomials of any degree $\leq r-1$. We show that the two methods have asymptotic series expansions and the orders of convergence can be further improved by multi-step Richardson extrapolation, where the calculation are repeated with each subinterval halved. These orders of convergence are preserved in the corresponding discrete methods obtained by calculating the integrals with a numerical quadrature formula. Numerical examples are given to validate the theoretical estimates.http://www.kjm-math.org/article_154688_a0b67d7bba3d4dc8dee6e7f19c1c27a6.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 Mathematics2423-47888220220701Weakly mid-$(p_{1},\ldots,p_{m})$-summing multilinear operators21922715469810.22034/kjm.2022.301446.2359ENAbdelhamidTallabUniversity of M'sila, Laboratoire d'Analyse Fonctionnelle et G\'{e}om\'{e}trie des Espaces, Box 166, Ichbilia, M'sila, 28000, AlgeriaAthmaneFerradiUniversity of M'sila, Laboratoire d'Analyse Fonctionnelle et G\'{e}om\'{e}trie des Espaces, Box 166, Ichbilia, M'sila, 28000, Algeria0000-0002-3622-2508Journal Article20210825In this paper, we introduce the new ideal of the weakly mid-$(p1,...,pm)$-summing multilinear operators as multilinear version of weakly mid-p- summing linear operators. Using the space of mid-p-summable sequences, we present a characterization given by summability property. Also, we give an analogue of the Pietsch domination theorem for this new class of operators.http://www.kjm-math.org/article_154698_3407c7ef72d03fe9c6e1e16544730029.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 Mathematics2423-47888220220701An algorithm for doubly unitary Laurent polynomials22823315469910.22034/kjm.2022.331453.2498ENIhsenYenguiDepartment of Mathematics, University of Sfax, 3000, Sfax, TunisiaFatenBen AmorDepartment of Mathematics, University of Sfax, 3000, Sfax, TunisiaJournal Article20220228We propose two algorithms that for any ring $R$, given a doubly unitary Laurent polynomial $g \in R[X,X^{-1} ]$, compute $h \in R[X,X^{-1}] $ such that $gh \in R[ X^{-1}+X ]$ and $gh$ is monic. The first algorithm is directly extracted from the classical proof. The second algorithm is more direct and simpler. It relies on a symmetrization technique.http://www.kjm-math.org/article_154699_1e825df489c67ed6d8154770fe2eec08.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 Mathematics2423-47888220220701Biderivations on trivial extension algebras23424215470010.22034/kjm.2022.270633.2161ENSedighehBarootkoobDepartment of Mathematics, Faculty of Basic Sciences, University of Bo-
jnord, P. O. Box 1339, Bojnord, IRAN.Ali AkbarKhadem-MaboudiDepartment of Biostatistics, School of Allied Medical Sciences, Shahid Beheshti University of Medical sciences, Tehran, IRAN.Journal Article20210127We investigate biderivations, inner biderivations and extremal biderivations on a trivial extensions algebra. Our results are examined for some special trivial extension algebras, such as triangular algebras and certain generalized matrix algebras, renovating some older results. We also study biderivations on a unital algebra with a nontrivial idempotent, extending a variety of results to some more general algebras.http://www.kjm-math.org/article_154700_d4ac9ba1b700c26fac6c17f67ec21c5c.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 Mathematics2423-47888220220701Orthogonal spline collocation methods for 1D-parabolic problems with interfaces24326015471610.22034/kjm.2022.286589.2263ENSantosh KumarBhalDepartment of Mathematics, School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, India0000-0001-8394-4821SnehalataBehuraDepartment of Mathematics, CIPET:IPT, Bhubaneswar-751024, India.Ashish KumarNandiMathematics Division, School of Advanced Sciences, Vellore Institute of Technology, Chennai, 600127, Tamil Nadu, India.Journal Article20210516Orthogonal spline collocation methods (OSC) are used to solve one dimensional heat conduction problems with interfaces. Cubic monomial basis functions are used to approximate the solution for spatial discretization and the Crank-Nicolson method for time stepping. Existence and uniqueness results are established for a discrete problem. This method is easily extended to monomials of higher degree. We present the results of experiments involving several examples which show the efficiency of OSC method. For both cubic and quartic basis functions, the results of numerical experiments demonstrate fourth-order accuracy in L∞ and L2 norms, and third-order accuracy in the<br />H1 norm. Moreover, sixth order superconvergence in nodal error of derivative of the OSC approximation for quartics is observed. OSC approach gives rise to almost block diagonal linear systems which are solved using standard software.http://www.kjm-math.org/article_154716_53417164f62805e6f80372cfaf7fd20d.pdf