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Journal of Inequalities and Applications最新文献

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Trace principle for Riesz potentials on Herz-type spaces and applications 赫兹型空间上里兹势的迹原理及其应用
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-09-03 DOI: 10.1186/s13660-024-03192-4
M. Ashraf Bhat, G. Sankara Raju Kosuru
{"title":"Trace principle for Riesz potentials on Herz-type spaces and applications","authors":"M. Ashraf Bhat, G. Sankara Raju Kosuru","doi":"10.1186/s13660-024-03192-4","DOIUrl":"https://doi.org/10.1186/s13660-024-03192-4","url":null,"abstract":"We establish trace inequalities for Riesz potentials on Herz-type spaces and examine the optimality of conditions imposed on specific parameters. We also present some applications in the form of Sobolev-type inequalities, including the Gagliardo–Nirenberg–Sobolev inequality and the fractional integration theorem in the Herz space setting. In addition, we obtain a Sobolev embedding theorem for Herz-type Sobolev spaces.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209590","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
Generalized Jensen and Jensen–Mercer inequalities for strongly convex functions with applications 强凸函数的广义詹森和詹森-默塞尔不等式及其应用
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-09-02 DOI: 10.1186/s13660-024-03189-z
Slavica Ivelić Bradanović, Neda Lovričević
{"title":"Generalized Jensen and Jensen–Mercer inequalities for strongly convex functions with applications","authors":"Slavica Ivelić Bradanović, Neda Lovričević","doi":"10.1186/s13660-024-03189-z","DOIUrl":"https://doi.org/10.1186/s13660-024-03189-z","url":null,"abstract":"Strongly convex functions as a subclass of convex functions, still equipped with stronger properties, are employed through several generalizations and improvements of the Jensen inequality and the Jensen–Mercer inequality. This paper additionally provides applications of obtained main results in the form of new estimates for so-called strong f-divergences: the concept of the Csiszár f-divergence for strongly convex functions f, together with particular cases (Kullback–Leibler divergence, $chi ^{2}$ -divergence, Hellinger divergence, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence.) Furthermore, new estimates for the Shannon entropy are obtained, and new Chebyshev-type inequalities are derived.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"261 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209591","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
Stability of functional inequality in digital metric space 数字度量空间中函数不等式的稳定性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-30 DOI: 10.1186/s13660-024-03179-1
Sundas Nawaz, Murad Khan Hassani, Afshan Batool, Ali Akgül
{"title":"Stability of functional inequality in digital metric space","authors":"Sundas Nawaz, Murad Khan Hassani, Afshan Batool, Ali Akgül","doi":"10.1186/s13660-024-03179-1","DOIUrl":"https://doi.org/10.1186/s13660-024-03179-1","url":null,"abstract":"In the present article, the Hyers–Ulam stability of the following inequality is analyzed: 0.1 $$ textstylebegin{cases} d (f(imath +jmath ), (f(imath )+ f(jmath )) )leq d (rho _{1}((f(imath +jmath )+ f(imath - jmath ), 2f(imath )) ) hphantom{ d (f(imath +jmath ), (f(imath )+ f(jmath )) )leq}{}+ d (rho _{2} (2f (frac{imath +jmath}{2} ), (f(imath )+ f(jmath )) ) ) end{cases} $$ in the setting of digital metric space, where $rho _{1}$ and $rho _{2}$ are fixed nonzero complex numbers with $1>sqrt{2}|rho _{1}|+|rho _{2}|$ by using fixed point and direct approach.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"156 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209593","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
Hybrid Hu-Storey type methods for large-scale nonlinear monotone systems and signal recovery 大规模非线性单调系统和信号恢复的混合 Hu-Storey 型方法
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-28 DOI: 10.1186/s13660-024-03187-1
Zoltan Papp, Sanja Rapajić, Abdulkarim Hassan Ibrahim, Supak Phiangsungnoen
{"title":"Hybrid Hu-Storey type methods for large-scale nonlinear monotone systems and signal recovery","authors":"Zoltan Papp, Sanja Rapajić, Abdulkarim Hassan Ibrahim, Supak Phiangsungnoen","doi":"10.1186/s13660-024-03187-1","DOIUrl":"https://doi.org/10.1186/s13660-024-03187-1","url":null,"abstract":"We propose two hybrid methods for solving large-scale monotone systems, which are based on derivative-free conjugate gradient approach and hyperplane projection technique. The conjugate gradient approach is efficient for large-scale systems due to low memory, while projection strategy is suitable for monotone equations because it enables simply globalization. The derivative-free function-value-based line search is combined with Hu-Storey type search directions and projection procedure, in order to construct globally convergent methods. Furthermore, the proposed methods are applied into solving a number of large-scale monotone nonlinear systems and reconstruction of sparse signals. Numerical experiments indicate the robustness of the proposed methods.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"42 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209594","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
Ulam–Hyers–Rassias Mittag-Leffler stability of ϖ–fractional partial differential equations ϖ-分式偏微分方程的 Ulam-Hyers-Rassias Mittag-Leffler 稳定性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-28 DOI: 10.1186/s13660-024-03170-w
Mohamed Rhaima, Djalal Boucenna, Lassaad Mchiri, Mondher Benjemaa, Abdellatif Ben Makhlouf
{"title":"Ulam–Hyers–Rassias Mittag-Leffler stability of ϖ–fractional partial differential equations","authors":"Mohamed Rhaima, Djalal Boucenna, Lassaad Mchiri, Mondher Benjemaa, Abdellatif Ben Makhlouf","doi":"10.1186/s13660-024-03170-w","DOIUrl":"https://doi.org/10.1186/s13660-024-03170-w","url":null,"abstract":"This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209597","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 solvability of a two-dimensional symmetric nonlinear system of difference equations 论二维对称非线性差分方程组的可解性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-27 DOI: 10.1186/s13660-024-03186-2
Stevo Stević, Bratislav Iričanin, Witold Kosmala, Zdeněk Šmarda
{"title":"On solvability of a two-dimensional symmetric nonlinear system of difference equations","authors":"Stevo Stević, Bratislav Iričanin, Witold Kosmala, Zdeněk Šmarda","doi":"10.1186/s13660-024-03186-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03186-2","url":null,"abstract":"We show that the system of difference equations $$ x_{n+k}=frac{x_{n+l}y_{n}-ef}{x_{n+l}+y_{n}-e-f},quad y_{n+k}= frac{y_{n+l}x_{n}-ef}{y_{n+l}+x_{n}-e-f},quad nin {mathbb{N}}_{0}, $$ where $kin {mathbb{N}}$ , $lin {mathbb{N}}_{0}$ , $l< k$ , $e, fin {mathbb{C}}$ , and $x_{j}, y_{j}in {mathbb{C}}$ , $j=overline{0,k-1}$ , is theoretically solvable and present some cases of the system when the general solutions can be found in a closed form.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209595","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 Bernstein and Turán-type integral mean estimates for polar derivative of a polynomial 论多项式极导数的伯恩斯坦和图兰型积分平均估计值
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-26 DOI: 10.1186/s13660-024-03183-5
Khangembam Babina Devi, Barchand Chanam
{"title":"On Bernstein and Turán-type integral mean estimates for polar derivative of a polynomial","authors":"Khangembam Babina Devi, Barchand Chanam","doi":"10.1186/s13660-024-03183-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03183-5","url":null,"abstract":"Let $p(z)$ be a polynomial of degree n having no zero in $|z|< k$ , $kleq 1$ , then Govil [Proc. Nat. Acad. Sci., 50(1980), 50-52] proved $$ max _{|z|=1}|p'(z)|leq frac{n}{1+k^{n}}max _{|z|=1}|p(z)|, $$ provided $|p'(z)|$ and $|q'(z)|$ attain their maxima at the same point on the circle $|z|=1$ , where $$ q(z)=z^{n}overline{pbigg(frac{1}{overline{z}}bigg)}. $$ In this paper, we present integral mean inequalities of Turán- and Erdös-Lax-type for the polar derivative of a polynomial by involving some coefficients of the polynomial, which refine some previously proved results and one of our results improves the above Govil inequality as a special case. These results incorporate the placement of the zeros and some coefficients of the underlying polynomial. Furthermore, we provide numerical examples and graphical representations to demonstrate the superior precision of our results compared to some previously established results.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"74 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209596","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
Existence of solution for some nonlinear g-Caputo fractional-order differential equations based on Wardowski–Mizoguchi–Takahashi contractions 基于 Wardowski-Mizoguchi-Takahashi 收缩的一些非线性 g-Caputo 分数阶微分方程解的存在性
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-23 DOI: 10.1186/s13660-024-03190-6
Babak Mohammadi, Vahid Parvaneh, Mohammad Mursaleen
{"title":"Existence of solution for some nonlinear g-Caputo fractional-order differential equations based on Wardowski–Mizoguchi–Takahashi contractions","authors":"Babak Mohammadi, Vahid Parvaneh, Mohammad Mursaleen","doi":"10.1186/s13660-024-03190-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03190-6","url":null,"abstract":"In this study, we prove the existence and uniqueness of a solution to a g-Caputo fractional differential equation with new boundary value conditions utilizing the combined Wardowski–Mizoguchi–Takahashi contractions via reduction of this equation to a fractional integral equation. We provide an example to demonstrate our findings.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"6 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209599","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 new Milne-type inequalities 一些新的米尔恩型不等式
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-23 DOI: 10.1186/s13660-024-03184-4
Paul Bosch, José M. Rodríguez, José M. Sigarreta, Eva Tourís
{"title":"Some new Milne-type inequalities","authors":"Paul Bosch, José M. Rodríguez, José M. Sigarreta, Eva Tourís","doi":"10.1186/s13660-024-03184-4","DOIUrl":"https://doi.org/10.1186/s13660-024-03184-4","url":null,"abstract":"Inequalities play a main role in pure and applied mathematics. In this paper, we prove a generalization of Milne inequality for any measure space. The argument in the proof of this inequality allows us to obtain other Milne-type inequalities. Also, we improve the discrete version of Milne inequality, which holds for any positive value of the parameter p. Finally, we present a Milne-type inequality in the fractional context.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209598","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 and lower solutions for an integral boundary problem with two different orders (left ( p,qright ) )-fractional difference 具有两种不同阶数的积分边界问题的上解和下解（左（p，右））--分数差分
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-08-14 DOI: 10.1186/s13660-024-03185-3
Mouataz Billah Mesmouli, Farah M. Al-Askar, Wael W. Mohammed
{"title":"Upper and lower solutions for an integral boundary problem with two different orders (left ( p,qright ) )-fractional difference","authors":"Mouataz Billah Mesmouli, Farah M. Al-Askar, Wael W. Mohammed","doi":"10.1186/s13660-024-03185-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03185-3","url":null,"abstract":"In this paper, a $left ( p,qright ) $ -fractional nonlinear difference equation of different orders is considered and discussed. With the help of $left ( p,qright ) $ -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142209600","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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