Pub Date : 2021-01-01DOI: 10.5666/KMJ.2021.61.2.257
A. H. Dar, M. Ahmad, J. Iqbal, Waseem Ali Mir
In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.
{"title":"Algorithm of Common Solutions to the Cayley Inclusion and Fixed Point Problems","authors":"A. H. Dar, M. Ahmad, J. Iqbal, Waseem Ali Mir","doi":"10.5666/KMJ.2021.61.2.257","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.2.257","url":null,"abstract":"In this paper, we develop an iterative algorithm for obtaining common solutions to the Cayley inclusion problem and the set of fixed points of a non-expansive mapping in Hilbert spaces. A numerical example is given for the justification of our claim.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70850178","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 : 2020-09-30DOI: 10.5666/KMJ.2020.60.3.485
Sung Guen Kim
{"title":"Extreme Points, Exposed Points and Smooth Points of the Space LS(2l∞3)","authors":"Sung Guen Kim","doi":"10.5666/KMJ.2020.60.3.485","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.3.485","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43038276","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 : 2020-09-30DOI: 10.5666/KMJ.2020.60.3.455
Pakorn Palakawong na Ayutthaya, B. Pibaljommee
{"title":"Purities of Ordered Ideals of Ordered Semirings","authors":"Pakorn Palakawong na Ayutthaya, B. Pibaljommee","doi":"10.5666/KMJ.2020.60.3.455","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.3.455","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45770232","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 : 2020-09-30DOI: 10.5666/KMJ.2020.60.3.599
K. Madani, S. Ouakkas
In this paper, we characterize a class of biharmonic maps from and between doubly product manifolds in terms of theie warping function. Examples are constructed when all of the factors are Euclidean spaces.
{"title":"Biharmonic Maps on Doubly Warped Product Manifolds","authors":"K. Madani, S. Ouakkas","doi":"10.5666/KMJ.2020.60.3.599","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.3.599","url":null,"abstract":"In this paper, we characterize a class of biharmonic maps from and between doubly product manifolds in terms of theie warping function. Examples are constructed when all of the factors are Euclidean spaces.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44312554","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 : 2020-09-30DOI: 10.5666/KMJ.2020.60.3.423
Erkko Lehtonen, N. Lekkoksung
{"title":"Variants of Essential Arity for Partial Functions","authors":"Erkko Lehtonen, N. Lekkoksung","doi":"10.5666/KMJ.2020.60.3.423","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.3.423","url":null,"abstract":"","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42282264","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 : 2020-03-31DOI: 10.5666/KMJ.2020.60.1.73
H. Srivastava
The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional “differintegral” equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind. Received February 1, 2019; revised October 7, 2019; accepted October 29, 2019. 2020 Mathematics Subject Classification: primary 26A33, 33B15, 33C05, 33C20, 33E12, 34A25, 44A10, secondary 33C65, 34A05, 34A08.
{"title":"Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments","authors":"H. Srivastava","doi":"10.5666/KMJ.2020.60.1.73","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.73","url":null,"abstract":"The subject of fractional calculus (that is, the calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past over four decades, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of mathematical, physical, engineering and statistical sciences. Various operators of fractional-order derivatives as well as fractional-order integrals do indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this survey-cum-expository article is to present a brief elementary and introductory overview of the theory of the integral and derivative operators of fractional calculus and their applications especially in developing solutions of certain interesting families of ordinary and partial fractional “differintegral” equations. This general talk will be presented as simply as possible keeping the likelihood of non-specialist audience in mind. Received February 1, 2019; revised October 7, 2019; accepted October 29, 2019. 2020 Mathematics Subject Classification: primary 26A33, 33B15, 33C05, 33C20, 33E12, 34A25, 44A10, secondary 33C65, 34A05, 34A08.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43238698","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 : 2020-03-31DOI: 10.5666/KMJ.2020.60.1.45
Canan Celep Yucel
A module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of M . In this work, we define a module M to be generalized FI-extending (GFI-extending) if for any fully invariant submodule N of M , there exists a direct summand D of M such that N ≤ D and that D/N is singular. The classes of FI-extending modules and singular modules are properly contained in the class of GFIextending modules. We first develop basic properties of this newly defined class of modules in the general module setting. Then, the GFI-extending property is shown to carry over to matrix rings. Finally, we show that the class of GFI-extending modules is closed under direct sums but not under direct summands. However, it is proved that direct summands are GFI-extending under certain restrictions.
{"title":"On Generalized FI-extending Modules","authors":"Canan Celep Yucel","doi":"10.5666/KMJ.2020.60.1.45","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.45","url":null,"abstract":"A module M is called FI-extending if every fully invariant submodule of M is essential in a direct summand of M . In this work, we define a module M to be generalized FI-extending (GFI-extending) if for any fully invariant submodule N of M , there exists a direct summand D of M such that N ≤ D and that D/N is singular. The classes of FI-extending modules and singular modules are properly contained in the class of GFIextending modules. We first develop basic properties of this newly defined class of modules in the general module setting. Then, the GFI-extending property is shown to carry over to matrix rings. Finally, we show that the class of GFI-extending modules is closed under direct sums but not under direct summands. However, it is proved that direct summands are GFI-extending under certain restrictions.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43875254","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 : 2020-03-31DOI: 10.5666/KMJ.2020.60.1.71
D. Heidari, B. Davvaz
A ring R is quasi-reversible if 0 6= ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].
{"title":"Quasi-reversibility of the Ring of 2×2 Matrices over an Arbitrary Field","authors":"D. Heidari, B. Davvaz","doi":"10.5666/KMJ.2020.60.1.71","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.71","url":null,"abstract":"A ring R is quasi-reversible if 0 6= ab ∈ I(R) for a, b ∈ R implies ba ∈ I(R), where I(R) is the set of all idempotents in R. In this short paper, we prove that the ring of 2×2 matrices over an arbitrary field is quasi-reversible, which is an answer to the question given by Da Woon Jung et al. in [Bull. Korean Math. Soc., 56(4) (2019) 993-1006].","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42428241","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 : 2020-03-31DOI: 10.5666/KMJ.2020.60.1.53
D. Dobbs
Let (A,M) ⊂ (B,N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N . Suppose henceforth that M ⊆ N . If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A+N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite
{"title":"Where Some Inert Minimal Ring Extensions of a Commutative Ring Come from","authors":"D. Dobbs","doi":"10.5666/KMJ.2020.60.1.53","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.53","url":null,"abstract":"Let (A,M) ⊂ (B,N) be commutative quasi-local rings. We consider the property that there exists a ring D such that A ⊆ D ⊂ B and the extension D ⊂ B is inert. Examples show that the number of such D may be any non-negative integer or infinite. The existence of such D does not imply M ⊆ N . Suppose henceforth that M ⊆ N . If the field extension A/M ⊆ B/N is algebraic, the existence of such D does not imply that B is integral over A (except when B has Krull dimension 0). If A/M ⊆ B/N is a minimal field extension, there exists a unique such D, necessarily given by D = A+N (but it need not be the case that N = MB). The converse fails, even if M = N and B/M is a finite","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49124197","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 : 2020-03-31DOI: 10.5666/KMJ.2020.60.1.177
A. Blaga, C. Dey
The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected αcosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature −α, provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.
{"title":"The Critical Point Equation on 3-dimensional α-cosymplectic Manifolds","authors":"A. Blaga, C. Dey","doi":"10.5666/KMJ.2020.60.1.177","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.1.177","url":null,"abstract":"The object of the present paper is to study the critical point equation (CPE) on 3-dimensional α-cosymplectic manifolds. We prove that if a 3-dimensional connected αcosymplectic manifold satisfies the Miao-Tam critical point equation, then the manifold is of constant sectional curvature −α, provided Dλ 6= (ξλ)ξ. We also give several interesting corollaries of the main result.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46625351","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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