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Positivity最新文献

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Positive solutions for nonlocal differential equations with concave and convex coefficients 具有凹凸系数的非局部微分方程的正解
IF 1 3区 数学
Positivity Pub Date : 2024-09-16 DOI: 10.1007/s11117-024-01086-9
Qingcong Song, Xinan Hao
{"title":"Positive solutions for nonlocal differential equations with concave and convex coefficients","authors":"Qingcong Song, Xinan Hao","doi":"10.1007/s11117-024-01086-9","DOIUrl":"https://doi.org/10.1007/s11117-024-01086-9","url":null,"abstract":"<p>In this paper, we study the positive solutions for nonlocal differential equations with concave and convex coefficients: </p><span>$$begin{aligned} -Aleft( int ^1_0 (u^p(s)+u^q(s))dsright) u''(t)=f(t,u(t)),quad tin (0,1), end{aligned}$$</span><p>where <span>(0&lt;p&lt;1le q.)</span> Using the fixed point index theory and fixed point theorems on cones, existence and multiplicity results are obtained, when the nonlinear term <i>f</i>(<i>t</i>, <i>x</i>) is continuous, has a singularity at <span>(x=0)</span>, changes sign, respectively.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new minimal element theorem and new generalizations of Ekeland’s variational principle in complete lattice optimization problem 完整晶格优化问题中新的最小元素定理和埃克兰德变分原理的新概括
IF 1 3区 数学
Positivity Pub Date : 2024-09-11 DOI: 10.1007/s11117-024-01083-y
Yousuke Araya, Wei-Shih Du
{"title":"A new minimal element theorem and new generalizations of Ekeland’s variational principle in complete lattice optimization problem","authors":"Yousuke Araya, Wei-Shih Du","doi":"10.1007/s11117-024-01083-y","DOIUrl":"https://doi.org/10.1007/s11117-024-01083-y","url":null,"abstract":"<p>In this paper, we first introduce some types of set relations on the power set of <i>n</i>-dimensional Euclidean spaces which are proposed by Kuroiwa–Tanaka–Ha and Jahn–Ha. We also mention new types of cancellation laws of set relations. Second, we introduce a complete lattice-valued problem on the power set of <i>n</i>-dimensional Euclidean spaces proposed by Hamel et al. Applying nonlinear scalarizing technique in complete lattice, we present a new type of minimal element theorem and generalized Ekeland’s variational principles in complete lattice optimization problem. We also present an existence theorem of minimal solutions related to the famous Takahashi’s minimization theorem in complete lattice optimization problem.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"68 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On representations and topological aspects of positive maps on non-unital quasi *- algebras 论非单元准*-代数上正映射的表征和拓扑问题
IF 1 3区 数学
Positivity Pub Date : 2024-09-06 DOI: 10.1007/s11117-024-01079-8
Giorgia Bellomonte, Bogdan Djordjević, Stefan Ivković
{"title":"On representations and topological aspects of positive maps on non-unital quasi *- algebras","authors":"Giorgia Bellomonte, Bogdan Djordjević, Stefan Ivković","doi":"10.1007/s11117-024-01079-8","DOIUrl":"https://doi.org/10.1007/s11117-024-01079-8","url":null,"abstract":"<p>In this paper we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras, thus extending the results from Bellomonte (GNS-construction for positive <span>(C^*-)</span>valued sesquilinear maps on a quasi <span>(*-)</span>algebra, Mediterr. J. Math., <b>21</b> 166 (22 pp) (2024)) to the case of non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals and noncommutative <span>(L^2)</span>-spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative <span>(L^2)</span>-space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142190111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A subgradient projection method for quasiconvex minimization 准凸最小化的子梯度投影法
IF 1 3区 数学
Positivity Pub Date : 2024-09-05 DOI: 10.1007/s11117-024-01082-z
Juan Choque, Felipe Lara, Raúl T. Marcavillaca
{"title":"A subgradient projection method for quasiconvex minimization","authors":"Juan Choque, Felipe Lara, Raúl T. Marcavillaca","doi":"10.1007/s11117-024-01082-z","DOIUrl":"https://doi.org/10.1007/s11117-024-01082-z","url":null,"abstract":"<p>In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By employing strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous, and strongly quasiconvex function (in the sense of Polyak in Soviet Math 7:72–75, 1966), under the same assumptions as those required for convex functions with the convex subdifferentials. Furthermore, a quasi-linear convergence rate of the iterates, extending similar results for the general quasiconvex case, is also provided.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"35 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A contribution to operators between Banach lattices 对巴拿赫网格间算子的贡献
IF 1 3区 数学
Positivity Pub Date : 2024-09-05 DOI: 10.1007/s11117-024-01081-0
Hassan Khabaoui, Jawad H’michane, Kamal El Fahri
{"title":"A contribution to operators between Banach lattices","authors":"Hassan Khabaoui, Jawad H’michane, Kamal El Fahri","doi":"10.1007/s11117-024-01081-0","DOIUrl":"https://doi.org/10.1007/s11117-024-01081-0","url":null,"abstract":"<p>In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattices and which brings together several classes of operators (as o-weakly compact, b-weakly compact, M-weakly compact, L-weakly compact and almost Dunford–Pettis operators). As applications, we find some new lattice approximation properties of these classes of operators. </p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"88 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some characterizations of almost order (L) sets and applications 近阶（L）集合的一些特征及其应用
IF 1 3区 数学
Positivity Pub Date : 2024-08-21 DOI: 10.1007/s11117-024-01078-9
Aziz Elbour, Fatima Zahrae El Hilali
{"title":"Some characterizations of almost order (L) sets and applications","authors":"Aziz Elbour, Fatima Zahrae El Hilali","doi":"10.1007/s11117-024-01078-9","DOIUrl":"https://doi.org/10.1007/s11117-024-01078-9","url":null,"abstract":"<p>The purpose of this paper is to establish several characterizations of almost order (L) sets (respectively, almost (L) sets). These characterizations generalize and correct those obtained recently by K. El Fahri and F.Z. Oughajji. In addition, we show that the almost (L) sets enjoy some interesting lattice approximation properties. Among other things, we show that a Banach lattice <i>E</i> has weakly sequentially continuous lattice operations if and only if the convex solid hull of every (L) set of <span>( E^{prime })</span> is an (L) set. Moreover, we study the domination property for absolutely weakly sequentially continuous operators.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"67 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new class of generalized Nash-population games via variational inequalities and fixed points 通过变式不等式和固定点的一类新的广义纳什人口博弈
IF 1 3区 数学
Positivity Pub Date : 2024-08-20 DOI: 10.1007/s11117-024-01080-1
Yue-tian Zhan, Xue-song Li, Nan-jing Huang
{"title":"A new class of generalized Nash-population games via variational inequalities and fixed points","authors":"Yue-tian Zhan, Xue-song Li, Nan-jing Huang","doi":"10.1007/s11117-024-01080-1","DOIUrl":"https://doi.org/10.1007/s11117-024-01080-1","url":null,"abstract":"<p>In this paper, we propose a new class of generalized Nash-population games (GNPGs) which can be used to capture the desired features of both population games (PGs) and generalized Nash games within the same framework. We introduce the concept of generalized inertial Nash equilibrium (GINE) for the GNPG and show the existence of GINE by using the method of the system of variational inequalities and fixed point theorems both in the compact and noncompact cases. Moreover, we introduce a slightly altruistic generalized inertial Nash equilibrium (SAGINE) as a refinement concept of the GINE and prove that the GNPG has at least an SAGINE under some mild assumptions.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Upper semi-Fredholm property of operators and their modulus on Banach lattices 巴拿赫网格上算子的上半弗雷德性质及其模数
IF 1 3区 数学
Positivity Pub Date : 2024-08-20 DOI: 10.1007/s11117-024-01075-y
Redouane Nouira, Othman Aboutafail, Youssef Ezzaki
{"title":"Upper semi-Fredholm property of operators and their modulus on Banach lattices","authors":"Redouane Nouira, Othman Aboutafail, Youssef Ezzaki","doi":"10.1007/s11117-024-01075-y","DOIUrl":"https://doi.org/10.1007/s11117-024-01075-y","url":null,"abstract":"<p>In the present manuscript, we present examples of regular upper semi-Fredholm (resp. non upper semi-Fredholm) operators on Banach lattices having non upper semi-Fredholm (resp. upper semi-Fredholm) modulus. We give also an example of a regular upper semi-Fredholm operator on Banach lattices with no modulus.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"30 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142189898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra 加权合成算子谱第 X 部分：多圆盘代数的加权自动形的谱和本质谱
IF 1 3区 数学
Positivity Pub Date : 2024-07-29 DOI: 10.1007/s11117-024-01069-w
Arkady Kitover, Mehmet Orhon
{"title":"Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra","authors":"Arkady Kitover, Mehmet Orhon","doi":"10.1007/s11117-024-01069-w","DOIUrl":"https://doi.org/10.1007/s11117-024-01069-w","url":null,"abstract":"<p>We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra <span>(mathbb {A}^n)</span>. In the case <span>(n=2)</span> we provide a detailed and, in most cases, complete description of these spectra.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"51 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-linear traces on semifinite factors and generalized singular values 半有限因子上的非线性迹线和广义奇异值
IF 1 3区 数学
Positivity Pub Date : 2024-07-24 DOI: 10.1007/s11117-024-01073-0
Masaru Nagisa, Yasuo Watatani
{"title":"Non-linear traces on semifinite factors and generalized singular values","authors":"Masaru Nagisa, Yasuo Watatani","doi":"10.1007/s11117-024-01073-0","DOIUrl":"https://doi.org/10.1007/s11117-024-01073-0","url":null,"abstract":"<p>We introduce non-linear traces of the Choquet type and Sugeno type on a semifinite factor <span>(mathcal {M})</span> as a non-commutative analog of the Choquet integral and Sugeno integral for non-additive measures. We need a weighted dimension function <span>(p mapsto alpha (tau (p)))</span> for projections <span>(p in mathcal {M})</span>, which is an analog of a monotone measure. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both the Choquet type and Sugeno type, respectively. Based on the notion of generalized eigenvalues and singular values, we show that non-linear traces of the Choquet type are closely related to the Lorentz function spaces and the Lorentz operator spaces if the weight functions <span>(alpha )</span> are concave. For the algebras of compact operators and factors of type <span>(textrm{II})</span>, we completely determine the condition that the associated weighted <span>(L^p)</span>-spaces for the non-linear traces become quasi-normed spaces in terms of the weight functions <span>(alpha )</span> for any <span>(0&lt; p &lt; infty )</span>. We also show that any non-linear trace of the Sugeno type yields a certain metric on the factor. This is an attempt at non-linear and non-commutative integration theory on semifinite factors.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":"167 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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