Pub Date : 2021-12-21DOI: 10.52737/18291163-2021.13.11-1-9
Jayanta Ghosh, D. Mandal, T. Samanta
In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship between the soft Jacobson radical of a ring and Jacobson semisimple ring is established. Some properties of this notion have been studied under homomorphism.
{"title":"The soft Jacobson radical of a commutative ring","authors":"Jayanta Ghosh, D. Mandal, T. Samanta","doi":"10.52737/18291163-2021.13.11-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.11-1-9","url":null,"abstract":"In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship between the soft Jacobson radical of a ring and Jacobson semisimple ring is established. Some properties of this notion have been studied under homomorphism.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46868143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-21DOI: 10.52737/18291163-2021.13.12-1-11
Sh. Navasardyan
The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $Phi$ and $Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $Psi$ and $Lambda$.
{"title":"Independence of the Axioms of Hypergroup over the Group","authors":"Sh. Navasardyan","doi":"10.52737/18291163-2021.13.12-1-11","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.12-1-11","url":null,"abstract":"The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $Phi$ and $Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $Psi$ and $Lambda$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43303500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-10DOI: 10.52737/18291163-2021.13.10-1-44
A. Poghosyan, Lusine Poghosyan, R. Barkhudaryan
We investigate the convergence of the quasi-periodic approximations in different frameworks and reveal exact asymptotic estimates of the corresponding errors. The estimates facilitate a fair comparison of the quasi-periodic approximations to other classical well-known approaches. We consider a special realization of the approximations by the inverse of the Vandermonde matrix, which makes it possible to prove the existence of the corresponding implementations, derive explicit formulas and explore convergence properties. We also show the application of polynomial corrections for the convergence acceleration of the quasi-periodic approximations. Numerical experiments reveal the auto-correction phenomenon related to the polynomial corrections so that utilization of approximate derivatives surprisingly results in better convergence compared to the expansions with the exact ones.
{"title":"On the Convergence of the Quasi-Periodic Approximations on a Finite Interval","authors":"A. Poghosyan, Lusine Poghosyan, R. Barkhudaryan","doi":"10.52737/18291163-2021.13.10-1-44","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.10-1-44","url":null,"abstract":"We investigate the convergence of the quasi-periodic approximations in different frameworks and reveal exact asymptotic estimates of the corresponding errors. The estimates facilitate a fair comparison of the quasi-periodic approximations to other classical well-known approaches. We consider a special realization of the approximations by the inverse of the Vandermonde matrix, which makes it possible to prove the existence of the corresponding implementations, derive explicit formulas and explore convergence properties. We also show the application of polynomial corrections for the convergence acceleration of the quasi-periodic approximations. Numerical experiments reveal the auto-correction phenomenon related to the polynomial corrections so that utilization of approximate derivatives surprisingly results in better convergence compared to the expansions with the exact ones.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44986222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-04DOI: 10.52737/18291163-2021.13.9-1-18
Bharat Bhushan, G. Sandhu, D. Kumar
In this paper, we consider skew Lie product on an involutive ring and study several algebraic identities for it, which include generalized derivations of the ring. The results give information about the commutativity of the ring and a description of the generalized derivations.
{"title":"Identities involving skew Lie product and a pair of generalized derivations in prime rings with involution","authors":"Bharat Bhushan, G. Sandhu, D. Kumar","doi":"10.52737/18291163-2021.13.9-1-18","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.9-1-18","url":null,"abstract":"In this paper, we consider skew Lie product on an involutive ring and study several algebraic identities for it, which include generalized derivations of the ring. The results give information about the commutativity of the ring and a description of the generalized derivations.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48685597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-04DOI: 10.52737/18291163-2021.13.8-1-21
Abdelouahab Mahmoudi, A. Kessi
In this paper, we study the existence and the Ulam stability of a solution to nonlinear backward impulsive differential equations with local or nonlocal conditions in Banach spaces. Using well-known classical fixed point theorems, we prove the existence of a solution. Subsequently, we prove the generalized Ulam-Hyers-Rassias stability of the solution to the problem. The obtained results are illustrated by some examples.
{"title":"Existence and Ulam Stability of Solution for Some Backward Impulsive Differential Equations on Banach Spaces","authors":"Abdelouahab Mahmoudi, A. Kessi","doi":"10.52737/18291163-2021.13.8-1-21","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.8-1-21","url":null,"abstract":"In this paper, we study the existence and the Ulam stability of a solution to nonlinear backward impulsive differential equations with local or nonlocal conditions in Banach spaces. Using well-known classical fixed point theorems, we prove the existence of a solution. Subsequently, we prove the generalized Ulam-Hyers-Rassias stability of the solution to the problem. The obtained results are illustrated by some examples.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46930813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-03DOI: 10.52737/18291163-2021.13.7-1-32
S. Husain, Mohd Asad, Mubashshir U. Khairoowala
The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.
{"title":"Strong convergence algorithm for the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem","authors":"S. Husain, Mohd Asad, Mubashshir U. Khairoowala","doi":"10.52737/18291163-2021.13.7-1-32","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.7-1-32","url":null,"abstract":"The purpose of this paper is to recommend an iterative scheme to approximate a common element of the solution sets of the split problem of variational inclusions, split generalized equilibrium problem and fixed point problem for non-expansive mappings. We prove that the sequences generated by the recommended iterative scheme strongly converge to a common element of solution sets of stated split problems. In the end, we provide a numerical example to support and justify our main result. The result studied in this paper generalizes and extends some widely recognized results in this direction.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44472464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-24DOI: 10.52737/18291163-2021.13.6-1-10
M. Grigoryan, A. Maranjyan
For any countable set $D subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]backslash D$.
{"title":"On the divergence of Fourier series in the general Haar system","authors":"M. Grigoryan, A. Maranjyan","doi":"10.52737/18291163-2021.13.6-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.6-1-10","url":null,"abstract":"For any countable set $D subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]backslash D$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45292389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-09-03DOI: 10.52737/18291163-2021.13.5-1-11
F. Hayrapetyan
For weighted $L^p$-classes of functions harmonic in the unit disc, we obtain a family of weighted integral representations with weight function of the type $|w|^{2varphi}cdot(1-|w|^{2rho})^{beta}$.
{"title":"Weighted integral representations of harmonic functions in the unit disc by means of Mittag-Leffler type kernels","authors":"F. Hayrapetyan","doi":"10.52737/18291163-2021.13.5-1-11","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.5-1-11","url":null,"abstract":"For weighted $L^p$-classes of functions harmonic in the unit disc, we obtain a family of weighted integral representations with weight function of the type $|w|^{2varphi}cdot(1-|w|^{2rho})^{beta}$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49083615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-23DOI: 10.52737/18291163-2021.13.4-1-10
M. Obradovic, N. Tuneski
Introducing a new method, we give sharp estimates of the Hermitian Toeplitz determinants of third order for the class S of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class S.
{"title":"Hermitian Toeplitz determinants for the class S of univalent functions","authors":"M. Obradovic, N. Tuneski","doi":"10.52737/18291163-2021.13.4-1-10","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.4-1-10","url":null,"abstract":"Introducing a new method, we give sharp estimates of the Hermitian Toeplitz determinants of third order for the class S of functions univalent in the unit disc. The new approach is also illustrated on some subclasses of the class S.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43935058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-15DOI: 10.52737/18291163-2021.13.3-1-20
G. C. Ugwunnadi
In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.
{"title":"Viscosity approximation method for solving variational inequality problem in real Banach spaces","authors":"G. C. Ugwunnadi","doi":"10.52737/18291163-2021.13.3-1-20","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.3-1-20","url":null,"abstract":"In this paper, we study the implicit and inertial-type viscosity approximation method for approximating a solution to the hierarchical variational inequality problem. Under some mild conditions on the parameters, we prove that the sequence generated by the proposed methods converges strongly to a solution of the above-mentioned problem in $q$-uniformly smooth Banach spaces. The results obtained in this paper generalize and improve many recent results in this direction.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42557416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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