Pub Date : 2021-10-02DOI: 10.5556/j.tkjm.53.2022.3639
B. Esmaeili, G. Haghighatdoost, F. Pashaie
It is well-known that some of minimal (or maximal) hypersurfaces are stable. However, there is growing recognition on unstable hypersurfaces by introducing the concept of index of stability for minimal ones. For instance, the index of stability for minimal hypersurefces in Euclidean n-sphere has been defined by J. Simons and followed by many people. Also, Barros and Sousa have studied a high order extention of index as the concept of r-index (i.e. index of r-stability) on r-minimal hypersurfaces of n-sphere. They gave low bonds for r-stability index of r-minimal hypersurfaces in Euclidean sphere. In this paper, we low bounds for the r-stability index of r-maximal closed spacelike hypersurfaces in the de Sitter space.
{"title":"r-Stablity Index of r-Maximal Closed Hypersurfaces in de Sitter Spaces","authors":"B. Esmaeili, G. Haghighatdoost, F. Pashaie","doi":"10.5556/j.tkjm.53.2022.3639","DOIUrl":"https://doi.org/10.5556/j.tkjm.53.2022.3639","url":null,"abstract":"It is well-known that some of minimal (or maximal) hypersurfaces are stable. However, there is growing recognition on unstable hypersurfaces by introducing the concept of index of stability for minimal ones. For instance, the index of stability for minimal hypersurefces in Euclidean n-sphere has been defined by J. Simons and followed by many people. Also, Barros and Sousa have studied a high order extention of index as the concept of r-index (i.e. index of r-stability) on r-minimal hypersurfaces of n-sphere. They gave low bonds for r-stability index of r-minimal hypersurfaces in Euclidean sphere. In this paper, we low bounds for the r-stability index of r-maximal closed spacelike hypersurfaces in the de Sitter space.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89543897","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 : 2021-06-15DOI: 10.5556/J.TKJM.23.1992.4522
Sharief Deshmukh
The normal bundle $bar nu$ of a totally real surface $M$ in $S^6$ splits as $barnu= JTMoplus barmu$ where $TM$ is the tangent bundle of $M$ and $barmu$ is subbundle of $barnu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic).
在$S^6$中，$M$的正常束$bar nu$分裂为$barnu= JTMoplus barmu$，其中$TM$是$M$的切线束，$barmu$是$barnu$的子束，$J$在几乎复杂的结构下是不变的。我们研究了具有恒定高斯曲率K的全实曲面M，其第二种基本形式为$h(x, y) in JTM$，并且我们证明了$K = 1$(即$M$是完全测地线)。
{"title":"TOTALLY REAL SURFACES IN $S^6$","authors":"Sharief Deshmukh","doi":"10.5556/J.TKJM.23.1992.4522","DOIUrl":"https://doi.org/10.5556/J.TKJM.23.1992.4522","url":null,"abstract":"\u0000 \u0000 \u0000The normal bundle $bar nu$ of a totally real surface $M$ in $S^6$ splits as $barnu= JTMoplus barmu$ where $TM$ is the tangent bundle of $M$ and $barmu$ is subbundle of $barnu$ which is invariant under the almost complex structure $J$. We study the totally real surfaces M of constant Gaussian curvature K for which the second fundamental form $h(x, y) in JTM$, and we show that $K = 1$ (that is, $M$ is totally geodesic). \u0000 \u0000 \u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"117 1 1","pages":"11-14"},"PeriodicalIF":0.6,"publicationDate":"2021-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83724976","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 : 2021-06-06DOI: 10.5556/J.TKJM.25.1994.4423
C. Adiga
We obtain Jacobi's two-square and four-square theorems as an application of an identity of L.J. Rogers.
作为罗杰斯恒等式的一个应用，我们得到了雅可比二平方定理和四平方定理。
{"title":"JACOBI'S TWO-SQUARE AND FOUR-SQUARE THEOREMS VIA ROGER'S IDENTITY","authors":"C. Adiga","doi":"10.5556/J.TKJM.25.1994.4423","DOIUrl":"https://doi.org/10.5556/J.TKJM.25.1994.4423","url":null,"abstract":"We obtain Jacobi's two-square and four-square theorems as an application of an identity of L.J. Rogers.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"110 1","pages":"37-40"},"PeriodicalIF":0.6,"publicationDate":"2021-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74189260","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 : 2021-05-25DOI: 10.5556/J.TKJM.29.1998.4289
T. Chern
Let J be a function meromorphic in the finite complex plane C. We donate by T(r, J)(To(r, !)) the Nevanlinna(Ahlfors-Shmizu) characteristic function of J. A mero morphic function a(z) (including the case f(z) == c where c in Cu {oo}) is called small with respect to f if T(r, a(z)) = o(T(r, J)) as r -, +oo. Ve let n(兀 0. This paper deals with the existence of the Borel directions concerning small functions for mermorphic functions of finite positive order. Using Tsuji's method, we shall mainly prove Theorem 1 stated in the abstract. Theorem~extends a result of Chuang [2, p.127, Corollary 5.3], there a(z} are restricte
{"title":"ON BOREL DIRECTION CONCERNING SMALL FUNCTIONS","authors":"T. Chern","doi":"10.5556/J.TKJM.29.1998.4289","DOIUrl":"https://doi.org/10.5556/J.TKJM.29.1998.4289","url":null,"abstract":"Let J be a function meromorphic in the finite complex plane C. We donate by T(r, J)(To(r, !)) the Nevanlinna(Ahlfors-Shmizu) characteristic function of J. A mero morphic function a(z) (including the case f(z) == c where c in Cu {oo}) is called small with respect to f if T(r, a(z)) = o(T(r, J)) as r -, +oo. Ve let n(兀 <p, a, J = a(z)) be the number of roots (multiple roots being counted with their multiplicities) of the equation j(z) = a(z) for z in the angular domain D(r,cp,a) = {z: largz 列< c..t, lzl < r} where 0 :::; cp < 21r, a > 0. This paper deals with the existence of the Borel directions concerning small functions for mermorphic functions of finite positive order. Using Tsuji's method, we shall mainly prove Theorem 1 stated in the abstract. Theorem~extends a result of Chuang [2, p.127, Corollary 5.3], there a(z} are restricte<l over all extended complex numbm·s. Chuang's method rs different from ours and is區ed on the existence of a sequence of filling disk with their roots in the works of Milloux [3] and Valiron [7].","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"169 1","pages":"13-16"},"PeriodicalIF":0.6,"publicationDate":"2021-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75671532","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 : 2021-05-16DOI: 10.5556/J.TKJM.28.1997.4247
L. Olszowy
In this paper we give an estimate of the modulus of near smoothness of the space $c_o(E_i)$. In the case of the space $c_o(l_{p_i})$ the exact formula for this modulus is derived. Moreover, we show that the properties of near uniform smoothness and local near uniform smoothness are hereditary with respect to the product space $c_o(E_i)$.
{"title":"LOCAL AND UNIFORM NEAR SMOOTHNESS OF SOME BANACH SPACES","authors":"L. Olszowy","doi":"10.5556/J.TKJM.28.1997.4247","DOIUrl":"https://doi.org/10.5556/J.TKJM.28.1997.4247","url":null,"abstract":"\u0000 \u0000 \u0000In this paper we give an estimate of the modulus of near smoothness of the space $c_o(E_i)$. In the case of the space $c_o(l_{p_i})$ the exact formula for this modulus is derived. Moreover, we show that the properties of near uniform smoothness and local near uniform smoothness are hereditary with respect to the product space $c_o(E_i)$. \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"227 1","pages":"253-263"},"PeriodicalIF":0.6,"publicationDate":"2021-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76879964","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 : 2021-05-12DOI: 10.5556/J.TKJM.30.1999.4210
Yin Dongsheng
{"title":"A GENERAL METHOD FOR C ONSTRUCTING REGULAR SUMMATION MATRIX","authors":"Yin Dongsheng","doi":"10.5556/J.TKJM.30.1999.4210","DOIUrl":"https://doi.org/10.5556/J.TKJM.30.1999.4210","url":null,"abstract":"","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"175 1","pages":"67-69"},"PeriodicalIF":0.6,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88830596","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 : 2021-05-05DOI: 10.5556/J.TKJM.53.2022.3411
Sapna Gahlot, R. Saraswat
There are many fuzzy information and divergence measures exist in the literature of fuzzy Information Theory. Inequalities play important role for finding the relations. Here, we will introduce some new information inequalities on fuzzy measures and their applications in pattern recognition. Also established relations between new and well known fuzzy divergence measures with help of the fuzzy $f$-divergence measure and jensen’s inequality.
{"title":"A New Fuzzy Information Inequalities and its Applications in Establishing Relation among Fuzzy $f$-Divergence Measures","authors":"Sapna Gahlot, R. Saraswat","doi":"10.5556/J.TKJM.53.2022.3411","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3411","url":null,"abstract":"\u0000\u0000\u0000There are many fuzzy information and divergence measures exist in the literature of fuzzy Information Theory. Inequalities play important role for finding the relations. Here, we will introduce some new information inequalities on fuzzy measures and their applications in pattern recognition. Also established relations between new and well known fuzzy divergence measures with help of the fuzzy $f$-divergence measure and jensen’s inequality. \u0000\u0000\u0000","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82695365","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 : 2021-05-01DOI: 10.5556/J.TKJM.30.1999.4229
Longyan Li, S. Cheng
where (Hl) f: (O,oo) -t Rand g: [O,oo) x [O,oo) -t Rare positive functions; and (H2) f is nondecreasing and g is nonincreasing in each of its independent variables. A positive fixed point x* that satisfies x = f(x)g(x, x) is also called a positive equi librium point of equation (1.1). Our objective of this note is to show that under mild conditions on the functions f and g, every real sequence in n tends to one of the positive equilibrium points of (1.1). Similar results have been obtained for a number of recureence relations, see e.g. Kocic and Ladas [1], Camouzis et al. [2], Li et al. [3], and Li [4]. Indeed, this note is motivated by a concern raised in Kocic and Ladas [1, p.46] related to the stability of recurrence relations.
{"title":"GLOBAL ATTRACTIVITY IN A FOUR-TERM RECURRENCE RELATION","authors":"Longyan Li, S. Cheng","doi":"10.5556/J.TKJM.30.1999.4229","DOIUrl":"https://doi.org/10.5556/J.TKJM.30.1999.4229","url":null,"abstract":"where (Hl) f: (O,oo) -t Rand g: [O,oo) x [O,oo) -t Rare positive functions; and (H2) f is nondecreasing and g is nonincreasing in each of its independent variables. A positive fixed point x* that satisfies x = f(x)g(x, x) is also called a positive equi librium point of equation (1.1). Our objective of this note is to show that under mild conditions on the functions f and g, every real sequence in n tends to one of the positive equilibrium points of (1.1). Similar results have been obtained for a number of recureence relations, see e.g. Kocic and Ladas [1], Camouzis et al. [2], Li et al. [3], and Li [4]. Indeed, this note is motivated by a concern raised in Kocic and Ladas [1, p.46] related to the stability of recurrence relations.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"1 1","pages":"223-229"},"PeriodicalIF":0.6,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76386478","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 : 2021-04-16DOI: 10.5556/J.TKJM.53.2022.3554
A. Ghaffari, S. Javadi, Ebrahim Tamimi
In this paper, we study Connes amenability of l-Munn algebras. We apply this results to semigroup algebras. We show that for a weakly cancellative semigroupS with finite idempotents, amenability and Connes amenability are equivalent.
{"title":"Connes Amenability of $l^1$-Munn Algebras","authors":"A. Ghaffari, S. Javadi, Ebrahim Tamimi","doi":"10.5556/J.TKJM.53.2022.3554","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3554","url":null,"abstract":"In this paper, we study Connes amenability of l-Munn algebras. We apply this results to semigroup algebras. We show that for a weakly cancellative semigroupS with finite idempotents, amenability and Connes amenability are equivalent.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"11 11","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72475070","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 : 2021-04-14DOI: 10.5556/J.TKJM.53.2022.3307
W. Khuangsatung, A. Kangtunyakarn
The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.
{"title":"A Method for Solving the Variational Inequality Problem and Fixed Point Problems in Banach Spaces","authors":"W. Khuangsatung, A. Kangtunyakarn","doi":"10.5556/J.TKJM.53.2022.3307","DOIUrl":"https://doi.org/10.5556/J.TKJM.53.2022.3307","url":null,"abstract":"The purpose of this research is to modify Halpern iteration’s process for finding a common element of the set of solutions of a variational inequality problem and the set of fixed points of a strictly pseudo contractive mapping in q-uniformly smooth Banach space. We also introduce a new technique to prove a strong convergence theorem for a finite family of strictly pseudo contractive mappings in q-uniformly smooth Banach space. Moreover, we give a numerical result to illustrate the main theorem.","PeriodicalId":45776,"journal":{"name":"Tamkang Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82494498","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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