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Approximation formulas related to Somos' quadratic recurrence constant. Somos二次递归常数的近似公式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-09-27 DOI: 10.1186/s13660-018-1859-8
Bo Zhang, Chao-Ping Chen
{"title":"Approximation formulas related to Somos' quadratic recurrence constant.","authors":"Bo Zhang,&nbsp;Chao-Ping Chen","doi":"10.1186/s13660-018-1859-8","DOIUrl":"https://doi.org/10.1186/s13660-018-1859-8","url":null,"abstract":"<p><p>We present two classes of asymptotic expansions related to Somos' quadratic recurrence constant and provide the recursive relations for determining the coefficients of each class of the asymptotic expansions by using Bell polynomials and other techniques. We also present continued fraction approximations related to Somos' quadratic recurrence constant.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"266"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1859-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36663590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triple Diamond-Alpha integral and Hölder-type inequalities. 三重菱形积分和Hölder-type不等式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-10 DOI: 10.1186/s13660-018-1704-0
Jing-Feng Tian
{"title":"Triple Diamond-Alpha integral and Hölder-type inequalities.","authors":"Jing-Feng Tian","doi":"10.1186/s13660-018-1704-0","DOIUrl":"https://doi.org/10.1186/s13660-018-1704-0","url":null,"abstract":"<p><p>In this paper, we first introduce the definition of triple Diamond-Alpha integral for functions of three variables. Therefore, we present the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral on time scales, and then we obtain some new generalizations of the Hölder and reverse Hölder inequalities for the triple Diamond-Alpha integral. Moreover, using the obtained results, we give a new generalization of the Minkowski inequality for the triple Diamond-Alpha integral on time scales.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"111"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1704-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36109941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
Admissibility of simultaneous prediction for actual and average values in finite population. 有限种群中实际值和平均值同时预测的容许性。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-16 DOI: 10.1186/s13660-018-1707-x
Chao Bai, Haiqi Li
{"title":"Admissibility of simultaneous prediction for actual and average values in finite population.","authors":"Chao Bai,&nbsp;Haiqi Li","doi":"10.1186/s13660-018-1707-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1707-x","url":null,"abstract":"<p><p>This paper studies the admissibility of simultaneous prediction of actual and average values of the regressand in the generalized linear regression model under the quadratic loss function. Necessary and sufficient conditions are derived for the simultaneous prediction to be admissible in classes of homogeneous and nonhomogeneous linear predictors, respectively.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"117"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1707-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36114855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Some majorization integral inequalities for functions defined on rectangles. 定义在矩形上的函数的几个最大化积分不等式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-27 DOI: 10.1186/s13660-018-1739-2
Shanhe Wu, Muhammad Adil Khan, Abdul Basir, Reza Saadati
{"title":"Some majorization integral inequalities for functions defined on rectangles.","authors":"Shanhe Wu,&nbsp;Muhammad Adil Khan,&nbsp;Abdul Basir,&nbsp;Reza Saadati","doi":"10.1186/s13660-018-1739-2","DOIUrl":"https://doi.org/10.1186/s13660-018-1739-2","url":null,"abstract":"<p><p>In this paper, we first prove an integral majorization theorem related to integral inequalities for functions defined on rectangles. We then apply the result to establish some new integral inequalities for functions defined on rectangles. The results obtained are generalizations of weighted Favard's inequality, which also provide a generalization of the results given by Maligranda et al. (J. Math. Anal. Appl. 190:248-262, 1995) in an earlier paper.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"146"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1739-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36312534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Sobolev's embedding on time scales. Sobolev在时间尺度上的嵌入。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-19 DOI: 10.1186/s13660-018-1730-y
Naveed Ahmad, Hira Ashraf Baig, Ghaus Ur Rahman, M Shoaib Saleem
{"title":"Sobolev's embedding on time scales.","authors":"Naveed Ahmad,&nbsp;Hira Ashraf Baig,&nbsp;Ghaus Ur Rahman,&nbsp;M Shoaib Saleem","doi":"10.1186/s13660-018-1730-y","DOIUrl":"https://doi.org/10.1186/s13660-018-1730-y","url":null,"abstract":"<p><p>For <math><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mi>n</mi></math> , the embeddings of Sobolev spaces <math><msubsup><mi>W</mi><mi>Δ</mi><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mi>Ω</mi><msup><mi>T</mi><mi>n</mi></msup></msub><mo>)</mo></math> of functions defined on an open subset of an arbitrary time scale <math><msup><mi>T</mi><mi>n</mi></msup></math> , <math><mi>n</mi><mo>≥</mo><mn>1</mn></math> , endowed with the Lebesgue Δ-measure have been developed in (Agarwal et al. in Adv. Differ. Equ. 2006:38121, 2006) for <math><mi>n</mi><mo>=</mo><mn>1</mn></math> and later generalized to arbitrary <math><mi>n</mi><mo>≥</mo><mn>1</mn></math> in (Su et al. in Dyn. Partial Differ. Equ. 12(3):241-263, 2015). In this article we present the embeddings of Sobolev spaces <math><msubsup><mi>W</mi><mi>Δ</mi><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mi>Ω</mi><msup><mi>T</mi><mi>n</mi></msup></msub><mo>)</mo></math> for <math><mi>n</mi><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>∞</mi></math> and then, using these embeddings, we develop general Sobolev's embedding for the Sobolev spaces <math><msubsup><mi>W</mi><mi>Δ</mi><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msubsup><mo>(</mo><msub><mi>Ω</mi><msup><mi>T</mi><mi>n</mi></msup></msub><mo>)</mo></math> on time scales, where <i>k</i> is a non-negative integer and <math><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mi>∞</mi></math> .</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"134"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1730-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The growth and approximation for an analytic function represented by Laplace-Stieltjes transforms with generalized order converging in the half plane. 用广义阶Laplace-Stieltjes变换表示的解析函数在半平面上收敛的增长与逼近。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-24 DOI: 10.1186/s13660-018-1783-y
Hong Yan Xu, Hua Wang
{"title":"The growth and approximation for an analytic function represented by Laplace-Stieltjes transforms with generalized order converging in the half plane.","authors":"Hong Yan Xu,&nbsp;Hua Wang","doi":"10.1186/s13660-018-1783-y","DOIUrl":"https://doi.org/10.1186/s13660-018-1783-y","url":null,"abstract":"<p><p>By utilizing the concept of generalized order, we investigate the growth of Laplace-Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace-Stieltjes transforms. Besides, we also study the problem on the approximation of this Laplace-Stieltjes transform and give some results about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms. Our results are extension and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"185"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1783-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A note on the almost-Schur lemma on smooth metric measure spaces. 光滑度量空间上的近似舒尔引理。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-27 DOI: 10.1186/s13660-018-1791-y
Jui-Tang Chen
{"title":"A note on the almost-Schur lemma on smooth metric measure spaces.","authors":"Jui-Tang Chen","doi":"10.1186/s13660-018-1791-y","DOIUrl":"https://doi.org/10.1186/s13660-018-1791-y","url":null,"abstract":"<p><p>In this paper, we prove almost-Schur inequalities on closed smooth metric measure spaces, which implies the results of Cheng and De Lellis-Topping whenever the weighted function <i>f</i> is constant.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"194"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1791-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem. 非线性抛物型最优控制问题的谱法后验误差估计。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-19 DOI: 10.1186/s13660-018-1729-4
Lin Li, Zuliang Lu, Wei Zhang, Fei Huang, Yin Yang
{"title":"A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem.","authors":"Lin Li,&nbsp;Zuliang Lu,&nbsp;Wei Zhang,&nbsp;Fei Huang,&nbsp;Yin Yang","doi":"10.1186/s13660-018-1729-4","DOIUrl":"https://doi.org/10.1186/s13660-018-1729-4","url":null,"abstract":"<p><p>In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete spectral approximation scheme by using the backward Euler scheme in time. Moreover, by using an orthogonal projection operator, we obtain <math><msup><mi>L</mi><mn>2</mn></msup><mo>(</mo><msup><mi>H</mi><mn>1</mn></msup><mo>)</mo><mo>-</mo><msup><mi>L</mi><mn>2</mn></msup><mo>(</mo><msup><mi>L</mi><mn>2</mn></msup><mo>)</mo></math> a posteriori error estimates of the approximation solutions for both the state and the control. Finally, by introducing two auxiliary equations, we also obtain <math><msup><mi>L</mi><mn>2</mn></msup><mo>(</mo><msup><mi>L</mi><mn>2</mn></msup><mo>)</mo><mo>-</mo><msup><mi>L</mi><mn>2</mn></msup><mo>(</mo><msup><mi>L</mi><mn>2</mn></msup><mo>)</mo></math> a posteriori error estimates of the approximation solutions for both the state and the control.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"138"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1729-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A Suzuki-type multivalued contraction on weak partial metric spaces and applications. 弱偏度量空间上的suzuki型多值收缩及其应用。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-10-05 DOI: 10.1186/s13660-018-1866-9
Hassen Aydi, M A Barakat, Zoran D Mitrović, Vesna Šešum-Čavić
{"title":"A Suzuki-type multivalued contraction on weak partial metric spaces and applications.","authors":"Hassen Aydi,&nbsp;M A Barakat,&nbsp;Zoran D Mitrović,&nbsp;Vesna Šešum-Čavić","doi":"10.1186/s13660-018-1866-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1866-9","url":null,"abstract":"<p><p>Based on a recent paper of Beg and Pathak (Vietnam J. Math. 46(3):693-706, 2018), we introduce the concept of <math><msubsup><mi>H</mi> <mi>q</mi> <mo>+</mo></msubsup> </math> -type Suzuki multivalued contraction mappings. We establish a fixed point theorem for this type of mappings in the setting of complete weak partial metric spaces. We also present an illustrated example. Moreover, we provide applications to a homotopy result and to an integral inclusion of Fredholm type. Finally, we suggest open problems for the class of 0-complete weak partial metric spaces, which is more general than complete weak partial metric spaces.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"270"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1866-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36620165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Noninstantaneous impulsive inequalities via conformable fractional calculus. 符合分数微积分的非瞬时脉冲不等式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-09-25 DOI: 10.1186/s13660-018-1855-z
Surang Sitho, Sotiris K Ntouyas, Praveen Agarwal, Jessada Tariboon
{"title":"Noninstantaneous impulsive inequalities via conformable fractional calculus.","authors":"Surang Sitho,&nbsp;Sotiris K Ntouyas,&nbsp;Praveen Agarwal,&nbsp;Jessada Tariboon","doi":"10.1186/s13660-018-1855-z","DOIUrl":"https://doi.org/10.1186/s13660-018-1855-z","url":null,"abstract":"<p><p>We establish some new noninstantaneous impulsive inequalities using the conformable fractional calculus.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"261"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1855-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36663591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 34
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