Pub Date : 2003-01-01DOI: 10.1155/S0161171203212369
B. Dhage, A. Asha, S. Kang
The present paper studies some common fixed-point theorems for pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000) and Rhoades (1996).
{"title":"ON COMMON FIXED POINTS OF PAIRS OF A SINGLE AND A MULTIVALUED COINCIDENTALLY COMMUTING MAPPINGS IN D-METRIC SPACES","authors":"B. Dhage, A. Asha, S. Kang","doi":"10.1155/S0161171203212369","DOIUrl":"https://doi.org/10.1155/S0161171203212369","url":null,"abstract":"The present paper studies some common fixed-point theorems for pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000) and Rhoades (1996).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203212369","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989100","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 : 2003-01-01DOI: 10.1155/S0161171203301139
P. Haukkanen
A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.
{"title":"Some characterizations of specially multiplicative functions","authors":"P. Haukkanen","doi":"10.1155/S0161171203301139","DOIUrl":"https://doi.org/10.1155/S0161171203301139","url":null,"abstract":"A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function fA such that f(m)f(n)=∑d|(m,n)f(mn/d2)fA(d) for all m and n. For example, the divisor functions and Ramanujan's τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203301139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989426","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 : 2003-01-01DOI: 10.1155/S0161171203303059
I. Vaisman
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family of compatible, local, Lagrangian functions. We give several examples and find the cohomological obstructions to globalization. Then, we extend the connections used in Finsler and Lagrange geometry, while giving an index-free presentation of these connections.
{"title":"Lagrange geometry on tangent manifolds","authors":"I. Vaisman","doi":"10.1155/S0161171203303059","DOIUrl":"https://doi.org/10.1155/S0161171203303059","url":null,"abstract":"Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a nondegenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper, we study a generalization which consists of replacing the tangent bundle by a general tangent manifold, and the Lagrangian by a family of compatible, local, Lagrangian functions. We give several examples and find the cohomological obstructions to globalization. Then, we extend the connections used in Finsler and Lagrange geometry, while giving an index-free presentation of these connections.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990084","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 : 2003-01-01DOI: 10.1155/S0161171203303321
G. Kohr
We deal with kernel convergence of domains in C n which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings on B.
{"title":"KERNEL CONVERGENCE AND BIHOLOMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES","authors":"G. Kohr","doi":"10.1155/S0161171203303321","DOIUrl":"https://doi.org/10.1155/S0161171203303321","url":null,"abstract":"We deal with kernel convergence of domains in C n which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and convex mappings on B.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990394","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 : 2003-01-01DOI: 10.1155/S0161171203303357
G. Szeto, L. Xue
Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*-Galois Azumaya extension of BH.
{"title":"ON HOPF GALOIS HIRATA EXTENSIONS","authors":"G. Szeto, L. Xue","doi":"10.1155/S0161171203303357","DOIUrl":"https://doi.org/10.1155/S0161171203303357","url":null,"abstract":"Let H be a finite-dimensional Hopf algebra over a field K, H* the dual Hopf algebra of H, and B a right H*-Galois and Hirata separable extension of BH. Then B is characterized in terms of the commutator subring VB(BH) of BH in B and the smash product VB(BH)#H. A sufficient condition is also given for B to be an H*-Galois Azumaya extension of BH.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303357","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990561","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 : 2003-01-01DOI: 10.1155/S0161171203306295
K. D. Magill
In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.
在之前的纸,我们确定所有这些拓扑nearrings𝒩n的添加剂组n维欧氏集团,1美元“xmlns: mml = " http://www.w3.org/1998/Math/MathML " > n > 1,和含有n维线性子空间我}{J = 1 n也对附近的理想的属性为每个w∈𝒩n,存在w我∈J, 1≤≤n,这样w = w w 1 + 2 +⋯+ w n和v w = w n为每个v∈𝒩n。在本文中，我们确定了这些近环的性质，它们的理想，当其中两个近环同构时，我们研究了这些近环的乘法半群。
{"title":"Some properties of linear right ideal nearrings","authors":"K. D. Magill","doi":"10.1155/S0161171203306295","DOIUrl":"https://doi.org/10.1155/S0161171203306295","url":null,"abstract":"In a previous paper, we determined all those topological nearrings 𝒩 n whose additive groups are the n -dimensional Euclidean groups, 1$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> n > 1 , and which contain n one-dimensional linear subspaces { J i } i = 1 n which are also right ideals of the nearring with the property that for each w ∈ 𝒩 n , there exist w i ∈ J i , 1 ≤ i ≤ n , such that w = w 1 + w 2 + ⋯ + w n and v w = v w n for each v ∈ 𝒩 n . In this paper, we determine the properties of these nearrings, their ideals, and when two of these nearrings are isomorphic, and we investigate the multiplicative semigroups of these nearrings.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203306295","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990834","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 : 2003-01-01DOI: 10.1155/S016117120301189X
M. Boulbrachene, M. Haiour, S. Saadi
We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs). Under W 2 , p ( Ω ) -regularity of the continuous solution, a quasi-optimal L ∞ -convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).
研究一类椭圆型拟变分不等式系统的数值分析。在w2, p (Ω) -连续解的正则性条件下，建立了分段线性有限元法的拟最优L∞收敛性，涉及到Bensoussan-Lions型单调算法和椭圆变分不等式(VIs)的标准一致误差估计。
{"title":"L∞-error estimate for a system of elliptic quasivariational inequalities","authors":"M. Boulbrachene, M. Haiour, S. Saadi","doi":"10.1155/S016117120301189X","DOIUrl":"https://doi.org/10.1155/S016117120301189X","url":null,"abstract":"We deal with the numerical analysis of a system of elliptic quasivariational inequalities (QVIs). Under W 2 , p ( Ω ) -regularity of the continuous solution, a quasi-optimal L ∞ -convergence of a piecewise linear finite element method is established, involving a monotone algorithm of Bensoussan-Lions type and standard uniform error estimates known for elliptic variational inequalities (VIs).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S016117120301189X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971365","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 : 2003-01-01DOI: 10.1155/S0161171203012250
Y. Kakihara
Asymptotically mean stationary (AMS) sources (probability measures) and channels are considered as an extension of stationary sources and channels. It is shown that each extreme point of the set of all AMS sources is ergodic, but not vice versa, and that each extreme point in the set of all AMS channels is ergodic, but not vice versa.
{"title":"ERGODICITY AND EXTREMALITY OF AMS SOURCES AND CHANNELS","authors":"Y. Kakihara","doi":"10.1155/S0161171203012250","DOIUrl":"https://doi.org/10.1155/S0161171203012250","url":null,"abstract":"Asymptotically mean stationary (AMS) sources (probability measures) and channels are considered as an extension of stationary sources and channels. It is shown that each extreme point of the set of all AMS sources is ergodic, but not vice versa, and that each extreme point in the set of all AMS channels is ergodic, but not vice versa.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203012250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971813","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 : 2003-01-01DOI: 10.1155/S0161171203208073
L. Hacia
Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and used in the theory of nonlinear hyperbolic differential equations.
{"title":"Applications of one- and two-dimensional Volterra inequalities in differential equations of the hyperbolic type.","authors":"L. Hacia","doi":"10.1155/S0161171203208073","DOIUrl":"https://doi.org/10.1155/S0161171203208073","url":null,"abstract":"Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and used in the theory of nonlinear hyperbolic differential equations.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203208073","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64981195","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 : 2003-01-01DOI: 10.1155/S0161171203208206
K. Neammanee
We use Stein's method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.
我们用斯坦因的方法来求柯西近似的边界。所考虑的随机变量必须是独立的。
{"title":"Cauchy approximation for sums of independent random variables","authors":"K. Neammanee","doi":"10.1155/S0161171203208206","DOIUrl":"https://doi.org/10.1155/S0161171203208206","url":null,"abstract":"We use Stein's method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203208206","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64981588","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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