Pub Date : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1169
V. Singhal, Rohit Mukherjee
. This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox’s H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large num-ber of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main (cid:12)ndings.
{"title":"On Certain Integral Transforms Involving Hypergeometric Functions and Struve Function","authors":"V. Singhal, Rohit Mukherjee","doi":"10.5666/KMJ.2016.56.4.1169","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1169","url":null,"abstract":". This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox’s H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large num-ber of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main (cid:12)ndings.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849917","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}
{"title":"h(x)-B-Tribonacci and h(x)-B-Tri Lucas polynomials","authors":"S. Arolkar, Y. S. Valaulikar","doi":"10.5666/KMJ.2016.56.4.1125","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1125","url":null,"abstract":"In this paper we introduce h(x)-B-Tribonacci and h(x)-B-Tri Lucas polynomials. We also obtain the identities for these polynomials.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849487","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 : 2016-12-23DOI: 10.5666/KMJ.2016.56.4.1207
T. Hwang, U. Ki, Hiroyuki Kurihara
Let M be a real hypersurface with constant mean curvature in a complex space form Mn(c), c ̸= 0. In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ with respect to the structure vector field ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor field φ, then M is a homogeneous real hypersurface of Type A.
设M为复空间中具有恒定平均曲率的实超曲面，其形式为Mn(c)， c (c) = 0。本文证明了如果结构Jacobi算子Rξ = R(·，ξ)ξ对结构向量场ξ为φ∇ξ -平行且Rξ与结构张量场φ可交换，则M是a型齐次实超曲面。
{"title":"Structure Jacobi Operators of Real Hypersurfaces with Constant Mean Curvature in a Complex Space Form","authors":"T. Hwang, U. Ki, Hiroyuki Kurihara","doi":"10.5666/KMJ.2016.56.4.1207","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.4.1207","url":null,"abstract":"Let M be a real hypersurface with constant mean curvature in a complex space form Mn(c), c ̸= 0. In this paper, we prove that if the structure Jacobi operator Rξ = R(·, ξ)ξ with respect to the structure vector field ξ is φ∇ξξ-parallel and Rξ commute with the structure tensor field φ, then M is a homogeneous real hypersurface of Type A.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849570","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.777
H. A. Agwa, A. Khodier, H. Ahmed
. In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term r )) σ t )) ) p t ) t ))) t ) , and ( r ( t ) x ∆ ( t )) ∆ + q ( t ) x ( t ) + p ( t ) f ( x ( σ ( t ))) = e ( t ) , on a time scale T , where r ( t ), p ( t ) and q ( t ) are real-valued right-dense continuous (rd-continuous) functions [1] defined on T with p ( t ) < 0 and τ : T → T is a strictly increasing differentiable function and lim t →∞ τ ( t ) = ∞ . No restriction is imposed on the forcing term e ( t ) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.
． 在本文中,我们建立了一些新的振动标准二阶强迫非线性阻尼项的功能动态方程r)σt))) p t) t)))),和(r (t) x∆(t)∆+ q (t) x (t) + p (t) f (x(σ(t))) = e (t),在一个时间尺度t r (t), p (t)和(t)是实值right-dense连续(rd-continuous)函数[1]上定义t和p (t) < 0和τ:T→T是一个严格递增可微函数，且任T→∞τ (T) =∞。没有对强迫项e (t)施加限制以满足Kartsatos条件。我们的结果推广和推广了一些先前的结果[5,8,10,11,12]，可以应用于一些以前没有讨论过的振荡问题。最后，我们给出了一些例子来说明我们的主要结果。
{"title":"Oscillation of Second-Order Nonlinear Forced Functional Dynamic Equations with Damping Term on Time Scales","authors":"H. A. Agwa, A. Khodier, H. Ahmed","doi":"10.5666/KMJ.2016.56.3.777","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.777","url":null,"abstract":". In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term r )) σ t )) ) p t ) t ))) t ) , and ( r ( t ) x ∆ ( t )) ∆ + q ( t ) x ( t ) + p ( t ) f ( x ( σ ( t ))) = e ( t ) , on a time scale T , where r ( t ), p ( t ) and q ( t ) are real-valued right-dense continuous (rd-continuous) functions [1] defined on T with p ( t ) < 0 and τ : T → T is a strictly increasing differentiable function and lim t →∞ τ ( t ) = ∞ . No restriction is imposed on the forcing term e ( t ) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849139","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.993
I. Jeong, G. Kim, Kyoung Nam Kim
. In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.
． 本文分别在实、复和四元数空间形式下给出了实超曲面的平行正规Jacobi算子的不存在性定理。
{"title":"Characterizations for Real Hypersurfaces in Complex and Quaternionic Space Forms Related to the Normal Jacobi Operator","authors":"I. Jeong, G. Kim, Kyoung Nam Kim","doi":"10.5666/KMJ.2016.56.3.993","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.993","url":null,"abstract":". In this paper we give some non-existence theorems for parallel normal Jacobi operator of real hypersurfaces in real, complex and quaternionic space forms, respectively.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849144","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.819
H. Habib, B. Belaïdi
In this paper, we study the order of growth of solutions to the nonhomogeneous linear differential equation f (k) +Ak−1e f (k−1) + · · ·+A1ef ′ +A0ef = F1e + F2e, where Aj (z) ( 6≡ 0) (j = 0, 1, · · · , k − 1), Fj (z) ( 6≡ 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a− b) 6= 0.
{"title":"On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations","authors":"H. Habib, B. Belaïdi","doi":"10.5666/KMJ.2016.56.3.819","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.819","url":null,"abstract":"In this paper, we study the order of growth of solutions to the nonhomogeneous linear differential equation f (k) +Ak−1e f (k−1) + · · ·+A1ef ′ +A0ef = F1e + F2e, where Aj (z) ( 6≡ 0) (j = 0, 1, · · · , k − 1), Fj (z) ( 6≡ 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a− b) 6= 0.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849257","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.727
C. John, B. Elavarasan
In this paper, we study and establish some interesting results of ideals in a poset. It is shown that for a nonzero ideal I of a poset P , there are at most two strongly prime ideals of P that are minimal over I. Also, we study the notion of primal ideals in a poset and the relationship among the primal ideals and strongly prime ideals is considered.
{"title":"Strongly Prime Ideals and Primal Ideals in Posets","authors":"C. John, B. Elavarasan","doi":"10.5666/KMJ.2016.56.3.727","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.727","url":null,"abstract":"In this paper, we study and establish some interesting results of ideals in a poset. It is shown that for a nonzero ideal I of a poset P , there are at most two strongly prime ideals of P that are minimal over I. Also, we study the notion of primal ideals in a poset and the relationship among the primal ideals and strongly prime ideals is considered.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849005","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.939
Jinwon Choi
. In this paper, we give an algorithm to construct a space curve in Euclidean 3-space E 3 from a plane curve which is called PDP-helix of order d . The notion of the PDP-helices is a generalization of a general helix and a slant helix in E 3 . It is naturally shown that the PDP-helix of order 1 and order 2 are the same as the general helix and the slant helix, respectively. We give a characterization of the PDP-helix of order d . Moreover, we study some geometric properties of that of order 3.
{"title":"A New Type of Helix Constructed by Plane Curves","authors":"Jinwon Choi","doi":"10.5666/KMJ.2016.56.3.939","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.939","url":null,"abstract":". In this paper, we give an algorithm to construct a space curve in Euclidean 3-space E 3 from a plane curve which is called PDP-helix of order d . The notion of the PDP-helices is a generalization of a general helix and a slant helix in E 3 . It is naturally shown that the PDP-helix of order 1 and order 2 are the same as the general helix and the slant helix, respectively. We give a characterization of the PDP-helix of order d . Moreover, we study some geometric properties of that of order 3.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849031","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.845
I. Işcan, M. Kunt
. In this paper, some Hermite-Hadamard-Fej(cid:19)er type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.
{"title":"Hermite-Hadamard-Fejér Type Inequalities for Harmonically Quasi-convex Functions via Fractional Integrals","authors":"I. Işcan, M. Kunt","doi":"10.5666/KMJ.2016.56.3.845","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.845","url":null,"abstract":". In this paper, some Hermite-Hadamard-Fej(cid:19)er type integral inequalities for harmonically quasi-convex functions in fractional integral forms have been obtained.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849276","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 : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.899
Seunghwan Baek, I. Jung, G. Exner, Chunji Li
. It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts W α with first two weights equal. Let α : 1 , 1 , √ x, ( √ u, √ v, √ w ) ∧ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let W α be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal W α satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.
． 已知半立方次非正常加权移位不需要满足平坦性，即两个权值相等迫使所有或几乎所有权值相等。因此，描述所有前两个权值相等的半立方次正规加权移位W α是一个很自然的问题。设α: 1,1，√x，(√u，√v，√w)∧为1 < x < u < v < w递归生成的权值序列的向后3步扩展，设w α为相应的权值移位。本文完整地刻画了满足正行列式系数附加假设的半立方次反常W α，所得结果与二次次反常的结果是平行的。
{"title":"On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights","authors":"Seunghwan Baek, I. Jung, G. Exner, Chunji Li","doi":"10.5666/KMJ.2016.56.3.899","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.899","url":null,"abstract":". It is known that a semi-cubically hyponormal weighted shift need not satisfy the flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe all semi-cubically hyponormal weighted shifts W α with first two weights equal. Let α : 1 , 1 , √ x, ( √ u, √ v, √ w ) ∧ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let W α be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal W α satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.","PeriodicalId":46188,"journal":{"name":"Kyungpook Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70849400","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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