Pub Date : 2022-05-27DOI: 10.5666/KMJ.2020.60.4.839
Alex Samuel Bamunoba, I. Kimuli, D. Ssevviiri
We define morphic near-ring elements and study their behavior in regular near-rings. We show that the class of left morphic regular near-rings is properly contained between the classes of left strongly regular and unit regular near-rings.
{"title":"Morphic Elements in Regular Near-rings","authors":"Alex Samuel Bamunoba, I. Kimuli, D. Ssevviiri","doi":"10.5666/KMJ.2020.60.4.839","DOIUrl":"https://doi.org/10.5666/KMJ.2020.60.4.839","url":null,"abstract":"We define morphic near-ring elements and study their behavior in regular near-rings. We show that the class of left morphic regular near-rings is properly contained between the classes of left strongly regular and unit regular near-rings.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45630202","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 : 2021-03-01DOI: 10.5666/KMJ.2021.61.1.75
O. Ahuja, N. Bohra, A. Çetinkaya, Sushil Kumar
In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.
{"title":"Univalent Functions Associated with the Symmetric Points and Cardioid-shaped Domain Involving (p,q)-calculus","authors":"O. Ahuja, N. Bohra, A. Çetinkaya, Sushil Kumar","doi":"10.5666/KMJ.2021.61.1.75","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.1.75","url":null,"abstract":"In this paper, we introduce new classes of post-quantum or (p, q)-starlike and convex functions with respect to symmetric points associated with a cardiod-shaped domain. We obtain (p, q)-Fekete-Szegö inequalities for functions in these classes. We also obtain estimates of initial (p, q)-logarithmic coefficients. In addition, we get q-Bieberbachde-Branges type inequalities for the special case of our classes when p = 1. Moreover, we also discuss some special cases of the obtained results.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47175163","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 : 2021-03-01DOI: 10.5666/KMJ.2021.61.1.49
S. N. Fathima, U. Pore
Abstract. Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper we obtain some congruences modulo 2, 4, 10 and 20 for the partition function EO(n). We give a simple proof of the first Ramanujan-type congruences EO (10n+ 8) ≡ 0 (mod 5) given by Andrews.
{"title":"Some Congruences for Andrews’ Partition Function EO(n)","authors":"S. N. Fathima, U. Pore","doi":"10.5666/KMJ.2021.61.1.49","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.1.49","url":null,"abstract":"Abstract. Recently, Andrews introduced partition functions EO(n) and EO(n) where the function EO(n) denotes the number of partitions of n in which every even part is less than each odd part and the function EO(n) denotes the number of partitions enumerated by EO(n) in which only the largest even part appears an odd number of times. In this paper we obtain some congruences modulo 2, 4, 10 and 20 for the partition function EO(n). We give a simple proof of the first Ramanujan-type congruences EO (10n+ 8) ≡ 0 (mod 5) given by Andrews.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49516321","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 : 2021-03-01DOI: 10.5666/KMJ.2021.61.1.139
Faouzi Haddouchi
Fractional calculus and fractional differential equations are recently experiencing rapid development. There are several notions of fractional derivatives, some classical, such as the Riemann-Liouville or Caputo definitions, and some novel, such as conformable fractional derivatives [18], β-derivatives [9], or others [12, 20]. Recently, the new definition of a conformable fractional derivative, given by [1, 2, 18], has drawn much interest from many researchers [6, 7, 17, 22, 23, 24, 26]. Recent results on conformable fractional differential equations can also be found in [3, 8, 11]. In 2017, X. Dong et al.[15] studied the existence and multiplicity of positive solutions for the following conformable fractional differential equation with p-Laplacian operator D(φp(D u(t))) = f(t, u(t)), 0 < t < 1, u(0) = u(1) = Du(0) = Du(1) = 0. Here, 1 < α ≤ 2 is a real number, D is the conformable fractional derivative, φp(s) = |s|p−2s, p > 1, φ−1 p = φq, 1/p+ 1/q = 1, and f : [0, 1]× [0,+∞)→ [0,+∞)
{"title":"Existence of Positive Solutions for a Class of Conformable Fractional Differential Equations with Parameterized Integral Boundary Conditions","authors":"Faouzi Haddouchi","doi":"10.5666/KMJ.2021.61.1.139","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.1.139","url":null,"abstract":"Fractional calculus and fractional differential equations are recently experiencing rapid development. There are several notions of fractional derivatives, some classical, such as the Riemann-Liouville or Caputo definitions, and some novel, such as conformable fractional derivatives [18], β-derivatives [9], or others [12, 20]. Recently, the new definition of a conformable fractional derivative, given by [1, 2, 18], has drawn much interest from many researchers [6, 7, 17, 22, 23, 24, 26]. Recent results on conformable fractional differential equations can also be found in [3, 8, 11]. In 2017, X. Dong et al.[15] studied the existence and multiplicity of positive solutions for the following conformable fractional differential equation with p-Laplacian operator D(φp(D u(t))) = f(t, u(t)), 0 < t < 1, u(0) = u(1) = Du(0) = Du(1) = 0. Here, 1 < α ≤ 2 is a real number, D is the conformable fractional derivative, φp(s) = |s|p−2s, p > 1, φ−1 p = φq, 1/p+ 1/q = 1, and f : [0, 1]× [0,+∞)→ [0,+∞)","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42221712","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.1.23
G. Chang, Hwankoo Kim
Let D be an integral domain with quotient field K, X an indeterminate over D, ∗ a star operation on D, and Cl∗(D) be the ∗-class group of D. The ∗w-operation on D is a star operation defined by I∗w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J∗ = D}. In this paper, we study two star operations {∗} and [∗] on D[X] defined by A{∗} = ⋂ P∈∗w-Max(D) ADP [X] and A [∗] = ( ⋂ P∈∗w-Max(D) AD[X]P [X]) ∩ AK[X]. Among other things, we show that Cl∗(D) ∼= Cl[∗](D[X]) if and only if D is integrally
{"title":"Two Extensions of a Star Operation on D to the Polynomial Ring D[X]","authors":"G. Chang, Hwankoo Kim","doi":"10.5666/KMJ.2021.61.1.23","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.1.23","url":null,"abstract":"Let D be an integral domain with quotient field K, X an indeterminate over D, ∗ a star operation on D, and Cl∗(D) be the ∗-class group of D. The ∗w-operation on D is a star operation defined by I∗w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J∗ = D}. In this paper, we study two star operations {∗} and [∗] on D[X] defined by A{∗} = ⋂ P∈∗w-Max(D) ADP [X] and A [∗] = ( ⋂ P∈∗w-Max(D) AD[X]P [X]) ∩ AK[X]. Among other things, we show that Cl∗(D) ∼= Cl[∗](D[X]) if and only if D is integrally","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":"70850082","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.2.279
J. R. Morales, E. Rojas
The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points. 1. Motivation In 1922, S. Banach [4] established his famous and fundamental result in the metric fixed point theory as follows: Theorem 1.1.(Banach Contraction Principle) Let (M, d) be a complete metric space and let S : M −→ M be a Banach contraction, that is, S satisfies that there exists α ∈ (0, 1) such that d(Sx, Sy) ≤ αd(x, y) (z1) for all x, y ∈M. Then, S has a unique fixed point in M. Notice that Banach’s contractions are continuous mappings, so, in the spirit to extend the BCP, in 1968, R. Kannan [11] introduced a new class of contractive mappings admitting discontinuous functions, as follows. * Corresponding Author. Received September 13, 2020; revised January 15, 2021; accepted January 19, 2021. 2020 Mathematics Subject Classification: 47H09, 47H10, 47J25.
{"title":"Generalized 𝜓-Geraghty-Zamfirescu Contraction Pairs in b-metric Spaces","authors":"J. R. Morales, E. Rojas","doi":"10.5666/KMJ.2021.61.2.279","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.2.279","url":null,"abstract":"The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points. 1. Motivation In 1922, S. Banach [4] established his famous and fundamental result in the metric fixed point theory as follows: Theorem 1.1.(Banach Contraction Principle) Let (M, d) be a complete metric space and let S : M −→ M be a Banach contraction, that is, S satisfies that there exists α ∈ (0, 1) such that d(Sx, Sy) ≤ αd(x, y) (z1) for all x, y ∈M. Then, S has a unique fixed point in M. Notice that Banach’s contractions are continuous mappings, so, in the spirit to extend the BCP, in 1968, R. Kannan [11] introduced a new class of contractive mappings admitting discontinuous functions, as follows. * Corresponding Author. Received September 13, 2020; revised January 15, 2021; accepted January 19, 2021. 2020 Mathematics Subject Classification: 47H09, 47H10, 47J25.","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":"70850195","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.2.309
Sang Dong Kim, Yong Hun Lee, B. Shin
A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.
{"title":"Conservative Upwind Correction Method for Scalar Linear Hyperbolic Equations","authors":"Sang Dong Kim, Yong Hun Lee, B. Shin","doi":"10.5666/KMJ.2021.61.2.309","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.2.309","url":null,"abstract":"A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.","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":"70850246","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.2.323
D. Kumar, M. Agarwal
Abstract. The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes’ [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy’s law. In this study, matching conditions were used at the fluid– fluid interface, whereas the B-J slip boundary condition was employed at the fluid–porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.
{"title":"MHD Pulsatile Flow and Heat Transfer of Two Immiscible Couple Stress Fluids Between Permeable Beds","authors":"D. Kumar, M. Agarwal","doi":"10.5666/KMJ.2021.61.2.323","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.2.323","url":null,"abstract":"Abstract. The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes’ [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy’s law. In this study, matching conditions were used at the fluid– fluid interface, whereas the B-J slip boundary condition was employed at the fluid–porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.","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":"70850258","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.2.213
G. D'este, D. K. Tütüncü
In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.
{"title":"Baer-Kaplansky Theorem for Modules over Non-commutative Algebras","authors":"G. D'este, D. K. Tütüncü","doi":"10.5666/KMJ.2021.61.2.213","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.2.213","url":null,"abstract":"In this paper we investigate the Baer-Kaplansky theorem for module classes on algebras of finite representation types over a field. To do this we construct finite dimensional quiver algebras over any field.","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":"70850126","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 : 2021-01-01DOI: 10.5666/KMJ.2021.61.1.169
Embarka Remli, A. Cherif
{"title":"On the Generalized of p-harmonic and f-harmonic Maps","authors":"Embarka Remli, A. Cherif","doi":"10.5666/KMJ.2021.61.1.169","DOIUrl":"https://doi.org/10.5666/KMJ.2021.61.1.169","url":null,"abstract":"","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":"70850070","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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