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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials. 第二类切比雪夫多项式和斐波那契多项式的有限积和。
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/s13660-018-1744-5
Taekyun Kim, Dae San Kim, Dmitry V Dolgy, Jin-Woo Park
{"title":"Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials.","authors":"Taekyun Kim,&nbsp;Dae San Kim,&nbsp;Dmitry V Dolgy,&nbsp;Jin-Woo Park","doi":"10.1186/s13660-018-1744-5","DOIUrl":"https://doi.org/10.1186/s13660-018-1744-5","url":null,"abstract":"<p><p>In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those sums of finite products in terms of Bernoulli polynomials and obtain some identities by using those expressions.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"148"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1744-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36311082","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: 24
Refining trigonometric inequalities by using Padé approximant. 用帕岱尔近似法改进三角不等式。
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/s13660-018-1742-7
Zhen Zhang, Huaqing Shan, Ligeng Chen
{"title":"Refining trigonometric inequalities by using Padé approximant.","authors":"Zhen Zhang,&nbsp;Huaqing Shan,&nbsp;Ligeng Chen","doi":"10.1186/s13660-018-1742-7","DOIUrl":"https://doi.org/10.1186/s13660-018-1742-7","url":null,"abstract":"<p><p>A two-point Padé approximant method is presented for refining some remarkable trigonometric inequalities including the Jordan inequality, Kober inequality, Becker-Stark inequality, and Wu-Srivastava inequality. Simple proofs are provided. It shows to achieve better approximation results than those of prevailing methods.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"149"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1742-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36311084","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
On a product-type operator between Hardy and α-Bloch spaces of the upper half-plane. 上半平面上Hardy与α-Bloch空间间的乘积型算子。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-10-10 DOI: 10.1186/s13660-018-1867-8
Stevo Stević, Ajay K Sharma
{"title":"On a product-type operator between Hardy and <i>α</i>-Bloch spaces of the upper half-plane.","authors":"Stevo Stević,&nbsp;Ajay K Sharma","doi":"10.1186/s13660-018-1867-8","DOIUrl":"https://doi.org/10.1186/s13660-018-1867-8","url":null,"abstract":"<p><p>Recently we have introduced a product-type operator and studied it on some spaces of analytic functions on the unit disc. Here we start investigating the operator on the space of analytic functions on the upper half-plane. We characterize the boundedness and compactness of the operator between Hardy and <i>α</i>-Bloch spaces on the domain.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"273"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1867-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36609580","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: 13
Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and exponential function. 用Liu-Owa积分算子和指数函数连接的解析函数的两个子类的多数化问题。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-10-11 DOI: 10.1186/s13660-018-1865-x
Huo Tang, Guantie Deng
{"title":"Majorization problems for two subclasses of analytic functions connected with the Liu-Owa integral operator and exponential function.","authors":"Huo Tang,&nbsp;Guantie Deng","doi":"10.1186/s13660-018-1865-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1865-x","url":null,"abstract":"<p><p>In the present paper, we investigate majorization properties for the class <math><msubsup><mi>M</mi> <mi>β</mi> <mi>α</mi></msubsup> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>γ</mi> <mo>)</mo></math> of uniformly starlike functions and the class <math><msubsup><mi>N</mi> <mi>β</mi> <mi>α</mi></msubsup> <mo>(</mo> <mi>p</mi> <mo>,</mo> <mi>θ</mi> <mo>)</mo></math> of spiral-like functions related to an exponential function, which are defined through the Liu-Owa integral operator <math><msubsup><mi>Q</mi> <mrow><mi>β</mi> <mo>,</mo> <mi>p</mi></mrow> <mi>α</mi></msubsup> </math> given by (1.5). Also, some special cases of our main results in a form of corollaries are shown.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"277"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1865-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36620176","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: 7
Modified hybrid decomposition of the augmented Lagrangian method with larger step size for three-block separable convex programming. 三块可分凸规划中较大步长增广拉格朗日方法的改进混合分解。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-10-04 DOI: 10.1186/s13660-018-1863-z
Min Sun, Yiju Wang
{"title":"Modified hybrid decomposition of the augmented Lagrangian method with larger step size for three-block separable convex programming.","authors":"Min Sun,&nbsp;Yiju Wang","doi":"10.1186/s13660-018-1863-z","DOIUrl":"https://doi.org/10.1186/s13660-018-1863-z","url":null,"abstract":"<p><p>The Jacobian decomposition and the Gauss-Seidel decomposition of augmented Lagrangian method (ALM) are two popular methods for separable convex programming. However, their convergence is not guaranteed for three-block separable convex programming. In this paper, we present a modified hybrid decomposition of ALM (MHD-ALM) for three-block separable convex programming, which first updates all variables by a hybrid decomposition of ALM, and then corrects the output by a correction step with constant step size <math><mi>α</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>2</mn> <mo>-</mo> <msqrt><mn>2</mn></msqrt> <mo>)</mo></math> which is much less restricted than the step sizes in similar methods. Furthermore, we show that <math><mn>2</mn> <mo>-</mo> <msqrt><mn>2</mn></msqrt> </math> is the optimal upper bound of the constant step size <i>α</i>. The rationality of MHD-ALM is testified by theoretical analysis, including global convergence, ergodic convergence rate, nonergodic convergence rate, and refined ergodic convergence rate. MHD-ALM is applied to solve video background extraction problem, and numerical results indicate that it is numerically reliable and requires less computation.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"269"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1863-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36621641","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
Approximate weakly efficient solutions of set-valued vector equilibrium problems. 集值向量平衡问题的近似弱有效解。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-20 DOI: 10.1186/s13660-018-1773-0
Jian Chen, Yihong Xu, Ke Zhang
{"title":"Approximate weakly efficient solutions of set-valued vector equilibrium problems.","authors":"Jian Chen,&nbsp;Yihong Xu,&nbsp;Ke Zhang","doi":"10.1186/s13660-018-1773-0","DOIUrl":"https://doi.org/10.1186/s13660-018-1773-0","url":null,"abstract":"<p><p>In this paper, we introduce a new kind of approximate weakly efficient solutions to the set-valued vector equilibrium problems with constraints in locally convex Hausdorff topological vector spaces; then we discuss a relationship between the weakly efficient solutions and approximate weakly efficient solutions. Under the assumption of near cone-subconvexlikeness, by using the separation theorem for convex sets we establish Kuhn-Tucker-type and Lagrange-type optimality conditions for set-valued vector equilibrium problems, respectively.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"181"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1773-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419170","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: 3
Wavelet density estimation for mixing and size-biased data. 混合和尺寸偏差数据的小波密度估计。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-25 DOI: 10.1186/s13660-018-1784-x
Junke Kou, Huijun Guo
{"title":"Wavelet density estimation for mixing and size-biased data.","authors":"Junke Kou,&nbsp;Huijun Guo","doi":"10.1186/s13660-018-1784-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1784-x","url":null,"abstract":"<p><p>This paper considers wavelet estimation for a multivariate density function based on mixing and size-biased data. We provide upper bounds for the mean integrated squared error (MISE) of wavelet estimators. It turns out that our results reduce to the corresponding theorem of Shirazi and Doosti (Stat. Methodol. 27:12-19, 2015), when the random sample is independent.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"189"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1784-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419178","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: 8
Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers. 由若干特殊数的生成函数导出奈万林纳特征函数的计算。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-07 DOI: 10.1186/s13660-018-1722-y
Serkan Araci, Mehmet Acikgoz
{"title":"Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers.","authors":"Serkan Araci,&nbsp;Mehmet Acikgoz","doi":"10.1186/s13660-018-1722-y","DOIUrl":"https://doi.org/10.1186/s13660-018-1722-y","url":null,"abstract":"<p><p>In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by <math><mi>n</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> and <math><mi>n</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>E</mi><mo>)</mo></math> , respectively. Secondly, we derive the mean value of a positive logarithm of generating functions of Bernoulli numbers and associated Euler numbers shown as <math><mi>m</mi><mo>(</mo><mn>2</mn><mi>π</mi><mo>,</mo><mi>B</mi><mo>)</mo></math> and <math><mi>m</mi><mo>(</mo><mi>π</mi><mo>,</mo><mi>E</mi><mo>)</mo></math> , respectively. From these properties, we find Nevanlinna characteristic functions which we stated in the paper. Finally, as an application, we show that the generating function of Bernoulli numbers is a <i>normal function</i>.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"128"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1722-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421026","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: 3
A time domain characterization of vector-valued subspace weak Gabor bi-frames. 向量值子空间弱Gabor双帧的时域表征。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-22 DOI: 10.1186/s13660-018-1733-8
Jing Zhao, Yun-Zhang Li
{"title":"A time domain characterization of vector-valued subspace weak Gabor bi-frames.","authors":"Jing Zhao,&nbsp;Yun-Zhang Li","doi":"10.1186/s13660-018-1733-8","DOIUrl":"https://doi.org/10.1186/s13660-018-1733-8","url":null,"abstract":"<p><p>The construction of bi-frames is a fundamental problem in frame theory. Due to their wide applications, the study of vector-valued frames and subspace frames has interested many mathematicians in recent years. In this paper, we introduce the weak Gabor bi-frame (WGBF) in vector-valued subspaces, characterize WGBFs on the time domain, and present some examples.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"144"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1733-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421814","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
About some exponential inequalities related to the sinc function. 关于一些与sinc函数有关的指数不等式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-28 DOI: 10.1186/s13660-018-1740-9
Marija Rašajski, Tatjana Lutovac, Branko Malešević
{"title":"About some exponential inequalities related to the sinc function.","authors":"Marija Rašajski,&nbsp;Tatjana Lutovac,&nbsp;Branko Malešević","doi":"10.1186/s13660-018-1740-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1740-9","url":null,"abstract":"<p><p>In this paper, we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents and inequalities with certain polynomial exponents. Also, we establish intervals in which these inequalities hold.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"150"},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1740-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421815","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: 17
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