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An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions 对具有非局部和积分边界条件的 Katugampola-Hilfer 分数 BVP 的新 Lyapunov 型不等式的研究
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2023-12-22 DOI: 10.1186/s13660-023-03070-5
S. T. Thabet, Imed Kedim
{"title":"An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions","authors":"S. T. Thabet, Imed Kedim","doi":"10.1186/s13660-023-03070-5","DOIUrl":"https://doi.org/10.1186/s13660-023-03070-5","url":null,"abstract":"","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138943940","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
The existence of nonnegative solutions for a nonlinear fractional q-differential problem via a different numerical approach. 用不同的数值方法研究非线性分数阶q微分问题非负解的存在性。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2021-01-01 Epub Date: 2021-04-23 DOI: 10.1186/s13660-021-02612-z
Mohammad Esmael Samei, Ahmad Ahmadi, Sayyedeh Narges Hajiseyedazizi, Shashi Kant Mishra, Bhagwat Ram
{"title":"The existence of nonnegative solutions for a nonlinear fractional <i>q</i>-differential problem via a different numerical approach.","authors":"Mohammad Esmael Samei,&nbsp;Ahmad Ahmadi,&nbsp;Sayyedeh Narges Hajiseyedazizi,&nbsp;Shashi Kant Mishra,&nbsp;Bhagwat Ram","doi":"10.1186/s13660-021-02612-z","DOIUrl":"https://doi.org/10.1186/s13660-021-02612-z","url":null,"abstract":"<p><p>This paper deals with the existence of nonnegative solutions for a class of boundary value problems of fractional <i>q</i>-differential equation <math><mmultiscripts><mi>D</mi> <mi>q</mi> <mi>σ</mi> <mprescripts></mprescripts> <none></none> <mi>c</mi></mmultiscripts> <mo>[</mo> <mi>k</mi> <mo>]</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <mi>w</mi> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>k</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>,</mo> <msup><mrow></mrow> <mi>c</mi></msup> <msubsup><mi>D</mi> <mi>q</mi> <mi>ζ</mi></msubsup> <mo>[</mo> <mi>k</mi> <mo>]</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo></math> with three-point conditions for <math><mi>t</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo></math> on a time scale <math><msub><mi>T</mi> <msub><mi>t</mi> <mn>0</mn></msub> </msub> <mo>=</mo> <mo>{</mo> <mi>t</mi> <mo>:</mo> <mi>t</mi> <mo>=</mo> <msub><mi>t</mi> <mn>0</mn></msub> <msup><mi>q</mi> <mi>n</mi></msup> <mo>}</mo> <mo>∪</mo> <mo>{</mo> <mn>0</mn> <mo>}</mo></math> , where <math><mi>n</mi> <mo>∈</mo> <mi>N</mi></math> , <math><msub><mi>t</mi> <mn>0</mn></msub> <mo>∈</mo> <mi>R</mi></math> , and <math><mn>0</mn> <mo><</mo> <mi>q</mi> <mo><</mo> <mn>1</mn></math> , based on the Leray-Schauder nonlinear alternative and Guo-Krasnoselskii theorem. Moreover, we discuss the existence of nonnegative solutions. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-021-02612-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38847880","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
Asymptotic dichotomy in a class of higher order nonlinear delay differential equations. 一类高阶非线性时滞微分方程的渐近二分类。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2019-01-01 Epub Date: 2019-01-07 DOI: 10.1186/s13660-018-1949-7
Yunhua Ye, Haihua Liang
{"title":"Asymptotic dichotomy in a class of higher order nonlinear delay differential equations.","authors":"Yunhua Ye,&nbsp;Haihua Liang","doi":"10.1186/s13660-018-1949-7","DOIUrl":"https://doi.org/10.1186/s13660-018-1949-7","url":null,"abstract":"<p><p>Employing a generalized Riccati transformation and integral averaging technique, we show that all solutions of the higher order nonlinear delay differential equation <dispformula> <math><msup><mi>y</mi> <mrow><mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> <mo>)</mo></mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mi>p</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <msup><mi>y</mi> <mrow><mo>(</mo> <mi>n</mi> <mo>)</mo></mrow> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mi>q</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mi>f</mi> <mrow><mo>(</mo> <mi>y</mi> <mrow><mo>(</mo> <mi>g</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo></mrow> <mo>)</mo></mrow> <mo>=</mo> <mn>0</mn></math> </dispformula> will converge to zero or oscillate, under some conditions listed in the theorems of the present paper. Several examples are also given to illustrate the applications of these results.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1949-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36884999","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
Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem. 两膜问题变分不等式的路径跟踪和半光滑牛顿法。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2019-01-01 Epub Date: 2019-01-05 DOI: 10.1186/s13660-019-1955-4
Shougui Zhang, Yueyue Yan, Ruisheng Ran
{"title":"Path-following and semismooth Newton methods for the variational inequality arising from two membranes problem.","authors":"Shougui Zhang,&nbsp;Yueyue Yan,&nbsp;Ruisheng Ran","doi":"10.1186/s13660-019-1955-4","DOIUrl":"https://doi.org/10.1186/s13660-019-1955-4","url":null,"abstract":"<p><p>A semismooth Newton method, based on variational inequalities and generalized derivative, is designed and analysed for unilateral contact problem between two membranes. The problem is first formulated as a corresponding regularized problem with a nonlinear function, which can be solved by the semismooth Newton method. We prove the convergence of the method in the function space. To improve the performance of the semismooth Newton method, we use the path-following method to adjust the parameter automatically. Finally, some numerical results are presented to illustrate the performance of the proposed method.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-019-1955-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36922961","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: 87
Lp-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in Rd 具有Rd中值的渐近负相关随机向量的lp收敛、完全收敛和弱大数定律
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-08 DOI: 10.1186/s13660-018-1699-6
Mi-Hwa Ko
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\"><ns0:math><ns0:msub><ns0:mi>L</ns0:mi><ns0:mi>p</ns0:mi></ns0:msub></ns0:math>-convergence, complete convergence, and weak laws of large numbers for asymptotically negatively associated random vectors with values in <ns0:math><ns0:msup><ns0:mi mathvariant=\"double-struck\">R</ns0:mi><ns0:mi>d</ns0:mi></ns0:msup></ns0:math>","authors":"Mi-Hwa Ko","doi":"10.1186/s13660-018-1699-6","DOIUrl":"https://doi.org/10.1186/s13660-018-1699-6","url":null,"abstract":"<p><p>In this paper, based on the Rosenthal-type inequality for asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>, we establish results on <math><msub><mi>L</mi><mi>p</mi></msub></math>-convergence and complete convergence of the maximums of partial sums are established. We also obtain weak laws of large numbers for coordinatewise asymptotically negatively associated random vectors with values in <math><msup><mi>R</mi><mi>d</mi></msup></math>.</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/s13660-018-1699-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36106420","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
Refined Wirtinger-type integral inequality. 改进的wirtinger型积分不等式。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-09 DOI: 10.1186/s13660-018-1700-4
Liansheng Zhang, Shuxia Wang
{"title":"Refined Wirtinger-type integral inequality.","authors":"Liansheng Zhang,&nbsp;Shuxia Wang","doi":"10.1186/s13660-018-1700-4","DOIUrl":"https://doi.org/10.1186/s13660-018-1700-4","url":null,"abstract":"<p><p>Based on the extreme value conditions of a multiple variables function, a new class of Wirtinger-type double integral inequality is established in this paper. The proposed inequality generalizes and refines the classical Wirtinger-based integral inequality and has less conservatism in comparison with Jensen's double integral inequality and other double integral inequalities in the literature. Thus, the stability criteria for delayed control systems derived by the proposed refined Wirtinger-type integral inequality are less conservative than existing results in the literature.</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/s13660-018-1700-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36106424","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
Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian. 一类包含分数阶p- laplace的kirchhoff型方程解的多重性和渐近性。
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/s13660-018-1708-9
Liejun Shen
{"title":"Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional <i>p</i>-Laplacian.","authors":"Liejun Shen","doi":"10.1186/s13660-018-1708-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1708-9","url":null,"abstract":"<p><p>The present study is concerned with the following fractional <i>p</i>-Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional <i>p</i>-Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.</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/s13660-018-1708-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36109939","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
A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations. 求解大规模无约束优化问题和非线性方程的共轭梯度算法。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-11 DOI: 10.1186/s13660-018-1703-1
Gonglin Yuan, Wujie Hu
{"title":"A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations.","authors":"Gonglin Yuan,&nbsp;Wujie Hu","doi":"10.1186/s13660-018-1703-1","DOIUrl":"https://doi.org/10.1186/s13660-018-1703-1","url":null,"abstract":"<p><p>For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan-Wei-Lu line search technique. It combines the steepest descent method with the famous conjugate gradient algorithm, which utilizes both the relevant function trait and the current point feature. It possesses the following properties: (i) the search direction has a sufficient descent feature and a trust region trait, and (ii) the proposed algorithm globally converges. Numerical results prove that the proposed algorithm is perfect compared with other similar optimization algorithms.</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/s13660-018-1703-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36114850","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
Analysis of stability for stochastic delay integro-differential equations. 随机时滞积分微分方程的稳定性分析。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-11 DOI: 10.1186/s13660-018-1702-2
Yu Zhang, Longsuo Li
{"title":"Analysis of stability for stochastic delay integro-differential equations.","authors":"Yu Zhang,&nbsp;Longsuo Li","doi":"10.1186/s13660-018-1702-2","DOIUrl":"https://doi.org/10.1186/s13660-018-1702-2","url":null,"abstract":"<p><p>In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the Euler-Maruyama method could reproduce the mean-square stability under a step-size constraint. We also confirm the mean-square stability of the split-step backward Euler method for nonlinear stochastic delay integro-differential equations. The numerical experiments further verify the theoretical results.</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/s13660-018-1702-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36114852","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
Generalization of the space l(p) derived by absolute Euler summability and matrix operators. 由绝对欧拉可和性和矩阵算子导出的空间l(p)的推广。
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-06-15 DOI: 10.1186/s13660-018-1724-9
Fadime Gökçe, Mehmet Ali Sarıgöl
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Generalization of the space <ns0:math><ns0:mi>l</ns0:mi><ns0:mo>(</ns0:mo><ns0:mi>p</ns0:mi><ns0:mo>)</ns0:mo></ns0:math> derived by absolute Euler summability and matrix operators.","authors":"Fadime Gökçe,&nbsp;Mehmet Ali Sarıgöl","doi":"10.1186/s13660-018-1724-9","DOIUrl":"https://doi.org/10.1186/s13660-018-1724-9","url":null,"abstract":"<p><p>The sequence space <math><mi>l</mi><mo>(</mo><mi>p</mi><mo>)</mo></math> having an important role in summability theory was defined and studied by Maddox (Q. J. Math. 18:345-355, 1967). In the present paper, we generalize the space <math><mi>l</mi><mo>(</mo><mi>p</mi><mo>)</mo></math> to the space <math><mo>|</mo><msubsup><mi>E</mi><mi>ϕ</mi><mi>r</mi></msubsup><mo>|</mo><mo>(</mo><mi>p</mi><mo>)</mo></math> derived by the absolute summability of Euler mean. Also, we show that it is a paranormed space and linearly isomorphic to <math><mi>l</mi><mo>(</mo><mi>p</mi><mo>)</mo></math> . Further, we determine <i>α</i>-, <i>β</i>-, and <i>γ</i>-duals of this space and construct its Schauder basis. Also, we characterize certain matrix operators on the space.</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/s13660-018-1724-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36285080","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
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