. This manuscript presents Hyers–Ulam stability and Hyers– Ulam–Rassias stability results of non–linear Volterra integro–delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of so-lutions. By means of abstract Gr¨onwall lemma, Gr¨onwall’s inequality on time scales, we establish Hyers–Ulam stability and Hyers–Ulam–Rassias stability results. There are some primary lemmas, inequalities and rele-vant assumptions that helps in our stability results.
{"title":"Hyers-Ulam Stability of Non-Linear Volterra Integro-Delay Dynamic System with Fractional Integrable Impulses on\u0000Time Scales","authors":"S. O. Shah, A. Zada","doi":"10.52547/ijmsi.17.1.85","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.85","url":null,"abstract":". This manuscript presents Hyers–Ulam stability and Hyers– Ulam–Rassias stability results of non–linear Volterra integro–delay dynamic system on time scales with fractional integrable impulses. Picard fixed point theorem is used for obtaining existence and uniqueness of so-lutions. By means of abstract Gr¨onwall lemma, Gr¨onwall’s inequality on time scales, we establish Hyers–Ulam stability and Hyers–Ulam–Rassias stability results. There are some primary lemmas, inequalities and rele-vant assumptions that helps in our stability results.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47416849","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}
. The QIF (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using WZ factorization. The WZ factorization can be faster than the LU factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer WZ and ZW factorizations by using the null space generators of some special nested submatrices of a matrix A .
{"title":"On the WZ Factorization of the Real and Integer Matrices","authors":"E. Golpar-Raboky, E. Babolian","doi":"10.52547/ijmsi.17.1.71","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.71","url":null,"abstract":". The QIF (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using WZ factorization. The WZ factorization can be faster than the LU factorization because, it performs the simultaneous evaluation of two columns or two rows. Here, we present a method for computing the real and integer WZ and ZW factorizations by using the null space generators of some special nested submatrices of a matrix A .","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48095185","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}
. In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.
{"title":"On Bernstein Type Inequalities for Complex Polynomial","authors":"M. Bidkham, E. KhojastehnezadZHAD","doi":"10.52547/ijmsi.17.1.111","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.111","url":null,"abstract":". In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41620588","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}
. As two-dimensional coupled system of nonlinear partial dif-ferential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numerical method based on Taylor series expansion and Haar wavelets is presented for solving coupled system of nonlinear partial differential equations. Efficiency and accuracy of the proposed method is depicted by comparing with classical methods.
{"title":"Modified Wavelet Method for Solving Two-dimensional Coupled System of Evolution Equations","authors":"I. Singh, S. Kumar","doi":"10.52547/ijmsi.17.1.239","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.239","url":null,"abstract":". As two-dimensional coupled system of nonlinear partial dif-ferential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numerical method based on Taylor series expansion and Haar wavelets is presented for solving coupled system of nonlinear partial differential equations. Efficiency and accuracy of the proposed method is depicted by comparing with classical methods.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42441804","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}
. Let G be a finite group and cd ∗ ( G ) be the set of nonlinear irreducible character degrees of G . Suppose that ρ ( G ) denotes the set of primes dividing some element of cd ∗ ( G ). The bipartite divisor graph for the set of character degrees which is denoted by B ( G ), is a bipartite graph whose vertices are the disjoint union of ρ ( G ) and cd ∗ ( G ), and a vertex p ∈ ρ ( G ) is connected to a vertex a ∈ cd ∗ ( G ) if and only if p | a . In this paper, we investigate the structure of a group G whose graph B ( G ) has five vertices. Especially we show that all these groups are solvable.
{"title":"Groups whose Bipartite Divisor Graph for Character Degrees Has Five Vertices","authors":"S. A. Moosavi","doi":"10.52547/ijmsi.17.1.145","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.145","url":null,"abstract":". Let G be a finite group and cd ∗ ( G ) be the set of nonlinear irreducible character degrees of G . Suppose that ρ ( G ) denotes the set of primes dividing some element of cd ∗ ( G ). The bipartite divisor graph for the set of character degrees which is denoted by B ( G ), is a bipartite graph whose vertices are the disjoint union of ρ ( G ) and cd ∗ ( G ), and a vertex p ∈ ρ ( G ) is connected to a vertex a ∈ cd ∗ ( G ) if and only if p | a . In this paper, we investigate the structure of a group G whose graph B ( G ) has five vertices. Especially we show that all these groups are solvable.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45460899","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}
. We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al [14]. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings as a subclass. The existence and convergence of coincidence-best and coincidence quasi-best proximity points in the setting of convex metric spaces are investigated.
{"title":"Coincidence Quasi-Best Proximity Points for Quasi-Cyclic-Noncyclic Mappings in Convex Metric Spaces","authors":"A. Abkar, M. Norouzian","doi":"10.52547/ijmsi.17.1.27","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.27","url":null,"abstract":". We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al [14]. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings as a subclass. The existence and convergence of coincidence-best and coincidence quasi-best proximity points in the setting of convex metric spaces are investigated.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46955287","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}
. Frames play significant role in various areas of science and en-gineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of K -frames for B ( H , K ) and we establish some result. Also, we consider the relationships between K -Frames and K -Operator Frames for B ( H ).
框架在科学和工程的各个领域发挥着重要作用。受Chander Shekhar，S.K.Kaushik和Abas Askarizadeh，Mohammad Ali Dehghan工作的启发，我们引入了B（H，K）的K-框架的概念，并建立了一些结果。此外，我们还考虑了B（H）的K-帧和K-算子帧之间的关系。
{"title":"Generalized Frames for B(H, K)","authors":"M. Rossafi, S. Kabbaj","doi":"10.52547/ijmsi.17.1.1","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.1","url":null,"abstract":". Frames play significant role in various areas of science and en-gineering. Motivated by the work of Chander Shekhar, S. K. Kaushik and Abas Askarizadeh, Mohammad Ali Dehghan, we introduce the concepts of K -frames for B ( H , K ) and we establish some result. Also, we consider the relationships between K -Frames and K -Operator Frames for B ( H ).","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47972670","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}
. The purpose of the present paper is to introduce a class D n Σ; δ C 0 ( α ) of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.
{"title":"Bi-concave Functions Defined by Al-Oboudi Differential Operator","authors":"Ş. Altınkaya","doi":"10.52547/ijmsi.17.1.207","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.207","url":null,"abstract":". The purpose of the present paper is to introduce a class D n Σ; δ C 0 ( α ) of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43529070","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}
. This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given products are proposed.
{"title":"Quaternionic Product of Circles and Cycles and Octonionic Product for Pairs of Circles","authors":"M. Crasmareanu","doi":"10.52547/ijmsi.17.1.227","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.227","url":null,"abstract":". This paper concerns with a product of circles induced by the quaternionic product considered in a projective manner. Several properties of this composition law are derived and on this way we arrive at some special numbers as roots or powers of unit. We extend this product to cycles as oriented circles and to pairs of circles by using the algebra of octonions. Three applications of the given products are proposed.","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47443517","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}
. In this paper, as a main result for Morrey spaces, we prove that the set M pq ( R n ) (cid:83) q
在本文中，作为Morrey空间的一个主要结果，我们证明了集合Mpq（Rn）（cid:83）q
{"title":"Spaceability on Morrey Spaces","authors":"Y. Sawano, S. M. Tabatabaie","doi":"10.52547/ijmsi.17.1.219","DOIUrl":"https://doi.org/10.52547/ijmsi.17.1.219","url":null,"abstract":". In this paper, as a main result for Morrey spaces, we prove that the set M pq ( R n ) (cid:83) q<r ≤ p M pr ( R n ) is spaceable in M pq ( R n ), where 0 < q < p < ∞ .","PeriodicalId":43670,"journal":{"name":"Iranian Journal of Mathematical Sciences and Informatics","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48501988","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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