Pub Date : 2016-09-23DOI: 10.5666/KMJ.2016.56.3.965
M. Atc̣eken
The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are obtained.
{"title":"Contact CR-Warped product Submanifolds in Cosymplectic Manifolds","authors":"M. Atc̣eken","doi":"10.5666/KMJ.2016.56.3.965","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.965","url":null,"abstract":"The aim of this paper is to study the geometry of contact CR-warped product submanifolds in a cosymplectic manifold. We search several fundamental properties of contact CR-warped product submanifolds in a cosymplectic manifold. We also give necessary and sufficient conditions for a submanifold in a cosymplectic manifold to be contact CR-(warped) product submanifold. After then we establish a general inequality between the warping function and the second fundamental for a contact CR-warped product submanifold in a cosymplectic manifold and consider contact CR-warped product submanifold in a cosymplectic manifold which satisfy the equality case of the inequality and some new results are 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":"70849089","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.2016.56.3.715
B. R. S. Kumar
In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.
本文利用Srinivasa Ramanujan给出的模方程，建立了一些新的P-Q型模方程。
{"title":"On Some Modular Equations in the Spirit of Ramanujan","authors":"B. R. S. Kumar","doi":"10.5666/KMJ.2016.56.3.715","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.715","url":null,"abstract":"In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.","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":"70849384","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.2016.56.3.831
H. Baek
In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.
{"title":"Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response","authors":"H. Baek","doi":"10.5666/KMJ.2016.56.3.831","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.831","url":null,"abstract":"In this paper, we consider a discrete predator-prey system with Watt-type functional response and impulsive controls. First, we find sufficient conditions for stability of a prey-free positive periodic solution of the system by using the Floquet theory and then prove the boundedness of the system. In addition, a condition for the permanence of the system is also obtained. Finally, we illustrate some numerical examples to substantiate our theoretical results, and display bifurcation diagrams and trajectories of some solutions of the system via numerical simulations, which show that impulsive controls can give rise to various kinds of dynamic behaviors.","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":"70849265","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.2016.56.3.867
H. Darwish, A. Y. Lashin, Soliman Mohammed Soileh
. The object of the present paper is to investigate the starlikeness of the class of functions f ( z ) = z p + ∞ (cid:80) = , , ... } ) which are analytic and p − valent in the unit disc U and satisfy the condition The starlikeness of certain integral operator are also discussed. The results obtained generalize the related works of some authors and some other new results are also obtained.
． 本文的目的是研究一类函数f (z) = z p +∞(cid:80) =，，，…})，在单位圆盘U上是解析的p -价的，并且满足某些积分算子的星形性。所得结果概括了一些作者的相关工作，并得到了一些新的结果。
{"title":"On Certain Subclasses of Starlike p-valent Functions","authors":"H. Darwish, A. Y. Lashin, Soliman Mohammed Soileh","doi":"10.5666/KMJ.2016.56.3.867","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.867","url":null,"abstract":". The object of the present paper is to investigate the starlikeness of the class of functions f ( z ) = z p + ∞ (cid:80) = , , ... } ) which are analytic and p − valent in the unit disc U and satisfy the condition The starlikeness of certain integral operator are also discussed. The results obtained generalize the related works of some authors and some other new results are also 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":"70849316","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.2016.56.3.951
A. Haseeb
The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.
本文的目的是研究Kenmotsu流形中关于半对称非度量连接的共圆曲率张量的一些新结果。
{"title":"On Concircular Curvature Tensor with respect to the Semi-symmetric Non-metric Connection in a Kenmotsu Manifold","authors":"A. Haseeb","doi":"10.5666/KMJ.2016.56.3.951","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.951","url":null,"abstract":"The objective of the present paper is to study some new results on concircular curvature tensor in a Kenmotsu manifold with respect to the semi-symmetric non-metric connection.","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":"70849044","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.2016.56.3.781
Sung Guen Kim
. Let d ∗ (1 , w ) 2 = R 2 with the octagonal norm of weight w . It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on d ∗ (1 , w ) 2 . We also show that the unit sphere of the space of symmetric bilinear forms on d ∗ (1 , w ) 2 is the disjoint union of the sets of smooth points, extreme points and the set A as follows: where the set A consists of ax 1 x 2 + by 1 y 2 + c ( x 1 y 2 + x 2 y 1 ) with ( a = b = 0 , c = ± 1 1+ w 2 ), ( a (cid:54) = b, ab ≥ 0 , c = 0), ( a = b, 0 < ac, 0 < | c | < | a | ), ( a (cid:54) = | c | , a = − b, 0 < ac, 0 < | c | ), ( a = 1 − w 1+ w , b = 0 , c = 1 1+ w ), ( a = 1+ w + w ( w 2 − 3) c 1+ w predual
． 设d * (1, w) 2 = r2，权w的八角范数。它是洛伦兹序列空间的二维实前元。本文对d * (1, w) 2上对称双线性空间的单位球的光滑点进行了分类。我们还证明了d * (1, w) 2上对称双线性形式空间的单位球是光滑点、极值点与集合A的集合的不相交并:ax的设置一个由1 x y 2 + 2 + 1 c (x 1 + x 2 y - 1)和(A = b = 0, c =±1 w 1 + 2), ((cid): 54) = b, ab≥0,c = 0)、(A = b, 0 < ac, 0 < c | | < | |), (c (cid): 54) = | |, A =−b, 0 < ac, 0 < c | |), (A = 1−w 1 + w, b = 0, c = 1 1 + w), (= 1 + w + w (w 2−3)c 1 + w预对偶
{"title":"The Geometry of the Space of Symmetric Bilinear Forms on ℝ 2 with Octagonal Norm","authors":"Sung Guen Kim","doi":"10.5666/KMJ.2016.56.3.781","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.781","url":null,"abstract":". Let d ∗ (1 , w ) 2 = R 2 with the octagonal norm of weight w . It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on d ∗ (1 , w ) 2 . We also show that the unit sphere of the space of symmetric bilinear forms on d ∗ (1 , w ) 2 is the disjoint union of the sets of smooth points, extreme points and the set A as follows: where the set A consists of ax 1 x 2 + by 1 y 2 + c ( x 1 y 2 + x 2 y 1 ) with ( a = b = 0 , c = ± 1 1+ w 2 ), ( a (cid:54) = b, ab ≥ 0 , c = 0), ( a = b, 0 < ac, 0 < | c | < | a | ), ( a (cid:54) = | c | , a = − b, 0 < ac, 0 < | c | ), ( a = 1 − w 1+ w , b = 0 , c = 1 1+ w ), ( a = 1+ w + w ( w 2 − 3) c 1+ w predual","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":"70849158","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.2016.56.3.911
Vivek Sahai, Ashish Verma
We obtain q–derivatives of Srivastava’s general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava’s triple q–hypergeometric series HA,q, HB,q and HC,q are also considered.
{"title":"nth-order q-derivatives of Srivastava`s General Triple q-hypergeometric Series with Respect to Parameters","authors":"Vivek Sahai, Ashish Verma","doi":"10.5666/KMJ.2016.56.3.911","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.911","url":null,"abstract":"We obtain q–derivatives of Srivastava’s general triple q-hypergeometric series with respect to its parameters. The particular cases leading to results for three Srivastava’s triple q–hypergeometric series HA,q, HB,q and HC,q are also 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":"70849411","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.2016.56.3.861
T. Subedi, A. M. Buhphang
A ring R called left SF if its simple left modules are flat. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semicommutative left SF-rings.
{"title":"On Left SF-Rings and Strongly Regular Rings","authors":"T. Subedi, A. M. Buhphang","doi":"10.5666/KMJ.2016.56.3.861","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.861","url":null,"abstract":"A ring R called left SF if its simple left modules are flat. Regular rings are known to be left SF-rings. However, till date it is unknown whether a left SF-ring is necessarily regular. In this paper, we prove the strong regularity of left (right) complement bounded left SF-rings. We also prove the strong regularity of a class of generalized semicommutative left SF-rings.","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":"70849469","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.2016.56.3.807
S. Muralisankar, K. Jeyabal
The aim of this paper is to introduce the notion of -compatible maps and obtain some common fixed point theorems. Also, our results generalize some well known fixed point theorems.
{"title":"Compatible Maps and Common Fixed Point Theorems","authors":"S. Muralisankar, K. Jeyabal","doi":"10.5666/kmj.2016.56.3.807","DOIUrl":"https://doi.org/10.5666/kmj.2016.56.3.807","url":null,"abstract":"The aim of this paper is to introduce the notion of -compatible maps and obtain some common fixed point theorems. Also, our results generalize some well known fixed point theorems.","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":"70849220","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.2016.56.3.877
Arun Kajla, P. Agrawal
. In the present article, we study some approximation properties of the Kantorovich type generalization of Sz´asz type operators involving Charlier polynomials introduced by S. Varma and F. Ta¸sdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A -statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.
{"title":"Szasz-Kantorovich Type Operators Based on Charlier Polynomials","authors":"Arun Kajla, P. Agrawal","doi":"10.5666/KMJ.2016.56.3.877","DOIUrl":"https://doi.org/10.5666/KMJ.2016.56.3.877","url":null,"abstract":". In the present article, we study some approximation properties of the Kantorovich type generalization of Sz´asz type operators involving Charlier polynomials introduced by S. Varma and F. Ta¸sdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A -statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.","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":"70849338","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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