Journal of Inequalities and Applications最新文献

{"title":"Generalized Jacobi-Weierstrass operators and Jacobi expansions.","authors":"José A Adell,&nbsp;Jorge Bustamante,&nbsp;Juan J Merino,&nbsp;José M Quesada","doi":"10.1186/s13660-018-1747-2","DOIUrl":"https://doi.org/10.1186/s13660-018-1747-2","url":null,"abstract":"<p><p>We present a realization for some <i>K</i>-functionals associated with Jacobi expansions in terms of generalized Jacobi-Weierstrass operators. Fractional powers of the operators as well as results concerning simultaneous approximation and Nikolskii-Stechkin type inequalities are also considered.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1747-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419161","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}

{"title":"Covering functionals of cones and double cones.","authors":"Senlin Wu,&nbsp;Ke Xu","doi":"10.1186/s13660-018-1785-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1785-9","url":null,"abstract":"<p><p>The least positive number <i>γ</i> such that a convex body <i>K</i> can be covered by <i>m</i> translates of <i>γK</i> is called the covering functional of <i>K</i> (with respect to <i>m</i>), and it is denoted by <math><msub><mi>Γ</mi><mi>m</mi></msub><mo>(</mo><mi>K</mi><mo>)</mo></math> . Estimating covering functionals of convex bodies is an important part of Chuanming Zong's quantitative program for attacking Hadwiger's covering conjecture. Estimations of covering functionals of cones and double cones, which are best possible for certain pairs of <i>m</i> and <i>K</i>, are presented.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1785-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419175","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}

{"title":"An improved approach for studying oscillation of second-order neutral delay differential equations.","authors":"Said R Grace,&nbsp;Jozef Džurina,&nbsp;Irena Jadlovská,&nbsp;Tongxing Li","doi":"10.1186/s13660-018-1767-y","DOIUrl":"https://doi.org/10.1186/s13660-018-1767-y","url":null,"abstract":"<p><p>The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1767-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419182","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}

{"title":"The modified split generalized equilibrium problem for quasi-nonexpansive mappings and applications.","authors":"Kanyarat Cheawchan,&nbsp;Atid Kangtunyakarn","doi":"10.1186/s13660-018-1716-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1716-9","url":null,"abstract":"<p><p>In this paper, we introduce a new problem, the modified split generalized equilibrium problem, which extends the generalized equilibrium problem, the split equilibrium problem and the split variational inequality problem. We introduce a new method of an iterative scheme <math><mo>{</mo><msub><mi>x</mi><mi>n</mi></msub><mo>}</mo></math> for finding a common element of the set of solutions of variational inequality problems and the set of common fixed points of a finite family of quasi-nonexpansive mappings and the set of solutions of the modified split generalized equilibrium problem without assuming a demicloseness condition and <math><msub><mi>T</mi><mi>ω</mi></msub><mo>:</mo><mo>=</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>ω</mi><mo>)</mo><mi>I</mi><mo>+</mo><mi>ω</mi><mi>T</mi></math> , where <i>T</i> is a quasi-nonexpansive mapping and <math><mi>ω</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mn>2</mn></mfrac><mo>)</mo></math> ; a difficult proof in the framework of Hilbert space. In addition, we give a numerical example to support our main result.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1716-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421020","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}

{"title":"Inequalities for the fractional convolution operator on differential forms.","authors":"Zhimin Dai,&nbsp;Huacan Li,&nbsp;Qunfang Li","doi":"10.1186/s13660-018-1768-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1768-x","url":null,"abstract":"<p><p>The purpose of this paper is to derive some Coifman type inequalities for the fractional convolution operator applied to differential forms. The Lipschitz norm and BMO norm estimates for this integral type operator acting on differential forms are also obtained.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1768-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421826","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}

{"title":"Binomial difference sequence spaces of fractional order.","authors":"Jian Meng,&nbsp;Liquan Mei","doi":"10.1186/s13660-018-1873-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1873-x","url":null,"abstract":"<p><p>In this paper, we introduce the sequence spaces <math><msubsup><mi>b</mi> <mn>0</mn> <mrow><mi>r</mi> <mo>,</mo> <mi>s</mi></mrow> </msubsup> <mo>(</mo> <msup><mi>∇</mi> <mrow><mo>(</mo> <mi>α</mi> <mo>)</mo></mrow> </msup> <mo>)</mo></math> , <math><msubsup><mi>b</mi> <mi>c</mi> <mrow><mi>r</mi> <mo>,</mo> <mi>s</mi></mrow> </msubsup> <mo>(</mo> <msup><mi>∇</mi> <mrow><mo>(</mo> <mi>α</mi> <mo>)</mo></mrow> </msup> <mo>)</mo></math> , and <math><msubsup><mi>b</mi> <mi>∞</mi> <mrow><mi>r</mi> <mo>,</mo> <mi>s</mi></mrow> </msubsup> <mo>(</mo> <msup><mi>∇</mi> <mrow><mo>(</mo> <mi>α</mi> <mo>)</mo></mrow> </msup> <mo>)</mo></math> . We investigate some functional properties, inclusion relations, and the <i>α</i>-, <i>β</i>-, <i>γ</i>-, and continuous duals of these sets.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1873-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36609640","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}

{"title":"Weighted arithmetic-geometric operator mean inequalities.","authors":"Jianming Xue","doi":"10.1186/s13660-018-1750-7","DOIUrl":"https://doi.org/10.1186/s13660-018-1750-7","url":null,"abstract":"<p><p>In this paper, we refine and generalize some weighted arithmetic-geometric operator mean inequalities due to Lin (Stud. Math. 215:187-194, 2013) and Zhang (Banach J. Math. Anal. 9:166-172, 2015) as follows: Let <i>A</i> and <i>B</i> be positive operators. If <math><mn>0</mn><mo><</mo><mi>m</mi><mo>≤</mo><mi>A</mi><mo>≤</mo><msup><mi>m</mi><mo>'</mo></msup><mo><</mo><msup><mi>M</mi><mo>'</mo></msup><mo>≤</mo><mi>B</mi><mo>≤</mo><mi>M</mi></math> or <math><mn>0</mn><mo><</mo><mi>m</mi><mo>≤</mo><mi>B</mi><mo>≤</mo><msup><mi>m</mi><mo>'</mo></msup><mo><</mo><msup><mi>M</mi><mo>'</mo></msup><mo>≤</mo><mi>A</mi><mo>≤</mo><mi>M</mi></math> , then for a positive unital linear map Φ, <dispformula><math><mtable><mtr><mtd><msup><mi>Φ</mi><mn>2</mn></msup><mo>(</mo><mi>A</mi><msub><mi>∇</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>≤</mo><msup><mrow><mo>[</mo><mfrac><mrow><mi>K</mi><mo>(</mo><mi>h</mi><mo>)</mo></mrow><mrow><mi>S</mi><mo>(</mo><msup><mi>h</mi><mrow><mo>'</mo><mi>r</mi></mrow></msup><mo>)</mo></mrow></mfrac><mo>]</mo></mrow><mn>2</mn></msup><msup><mi>Φ</mi><mn>2</mn></msup><mo>(</mo><mi>A</mi><msub><mi>♯</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mi>Φ</mi><mn>2</mn></msup><mo>(</mo><mi>A</mi><msub><mi>∇</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>≤</mo><msup><mrow><mo>[</mo><mfrac><mrow><mi>K</mi><mo>(</mo><mi>h</mi><mo>)</mo></mrow><mrow><mi>S</mi><mo>(</mo><msup><mi>h</mi><mrow><mo>'</mo><mi>r</mi></mrow></msup><mo>)</mo></mrow></mfrac><mo>]</mo></mrow><mn>2</mn></msup><msup><mrow><mo>[</mo><mi>Φ</mi><mo>(</mo><mi>A</mi><mo>)</mo><msub><mi>♯</mi><mi>α</mi></msub><mi>Φ</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>]</mo></mrow><mn>2</mn></msup><mo>,</mo></mtd></mtr><mtr><mtd><msup><mi>Φ</mi><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><msub><mi>∇</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mn>16</mn></mfrac><msup><mrow><mo>[</mo><mfrac><mrow><msup><mi>K</mi><mn>2</mn></msup><mo>(</mo><mi>h</mi><mo>)</mo><msup><mrow><mo>(</mo><msup><mi>M</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mn>2</mn></msup></mrow><mrow><msup><mi>S</mi><mn>2</mn></msup><mo>(</mo><msup><mi>h</mi><mrow><mo>'</mo><mi>r</mi></mrow></msup><mo>)</mo><msup><mi>M</mi><mn>2</mn></msup><msup><mi>m</mi><mn>2</mn></msup></mrow></mfrac><mo>]</mo></mrow><mi>p</mi></msup><msup><mi>Φ</mi><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><msub><mi>♯</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msup><mi>Φ</mi><mrow><mn>2</mn><mi>p</mi></mrow></msup><mo>(</mo><mi>A</mi><msub><mi>∇</mi><mi>α</mi></msub><mi>B</mi><mo>)</mo><mo>≤</mo><mfrac><mrow><mn>1</mn></mrow><mn>16</mn></mfrac><msup><mrow><mo>[</mo><mfrac><mrow><msup><mi>K</mi><mn>2</mn></msup><mo>(</mo><mi>h</mi><mo>)</mo><msup><mrow><mo>(</mo><msup><mi>M</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>)</mo></mrow><mn>2</mn></msup></mrow><mrow><msup><m","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1750-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36344646","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}

{"title":"Inequalities and asymptotic expansions related to the generalized Somos quadratic recurrence constant.","authors":"Xue-Si Ma,&nbsp;Chao-Ping Chen","doi":"10.1186/s13660-018-1741-8","DOIUrl":"https://doi.org/10.1186/s13660-018-1741-8","url":null,"abstract":"<p><p>In this paper, we give asymptotic expansions and inequalities related to the generalized Somos quadratic recurrence constant, using its relation with the generalized Euler constant.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1741-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36311080","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}

{"title":"Well-posedness for a class of generalized variational-hemivariational inequalities involving set-valued operators.","authors":"Caijing Jiang","doi":"10.1186/s13660-018-1776-x","DOIUrl":"https://doi.org/10.1186/s13660-018-1776-x","url":null,"abstract":"<p><p>The aim of present work is to study some kinds of well-posedness for a class of generalized variational-hemivariational inequality problems involving set-valued operators. Some systematic approaches are presented to establish some equivalence theorems between several classes of well-posedness for the inequality problems and some corresponding metric characterizations, which generalize many known results. Finally, the well-posedness for a class of generalized mixed equilibrium problems is also considered.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1776-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36419176","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}

{"title":"The modified proximal point algorithm in Hadamard spaces.","authors":"Shih-Sen Chang,&nbsp;Lin Wang,&nbsp;Ching-Feng Wen,&nbsp;Jian Qiang Zhang","doi":"10.1186/s13660-018-1713-z","DOIUrl":"https://doi.org/10.1186/s13660-018-1713-z","url":null,"abstract":"<p><p>The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1713-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36421023","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}