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The learning performance of the weak rescaled pure greedy algorithms 弱重标纯粹贪婪算法的学习性能
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-03-04 DOI: 10.1186/s13660-024-03077-6
Qin Guo, Xianghua Liu, Peixin Ye
{"title":"The learning performance of the weak rescaled pure greedy algorithms","authors":"Qin Guo, Xianghua Liu, Peixin Ye","doi":"10.1186/s13660-024-03077-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03077-6","url":null,"abstract":"We investigate the regression problem in supervised learning by means of the weak rescaled pure greedy algorithm (WRPGA). We construct learning estimator by applying the WRPGA and deduce the tight upper bounds of the K-functional error estimate for the corresponding greedy learning algorithms in Hilbert spaces. Satisfactory learning rates are obtained under two prior assumptions on the regression function. The application of the WRPGA in supervised learning considerably reduces the computational cost while maintaining its powerful generalization capability when compared with other greedy learning algorithms.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"57 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036811","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 best constant for inequality involving the sum of the reciprocals and product of positive numbers with unit sum 涉及单位和的正数倒数之和与积的不等式的最佳常数
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-03-01 DOI: 10.1186/s13660-024-03107-3
Yagub N. Aliyev
{"title":"The best constant for inequality involving the sum of the reciprocals and product of positive numbers with unit sum","authors":"Yagub N. Aliyev","doi":"10.1186/s13660-024-03107-3","DOIUrl":"https://doi.org/10.1186/s13660-024-03107-3","url":null,"abstract":"In this paper, we study a special algebraic inequality containing a parameter, the sum of reciprocals and the product of positive real numbers whose sum is 1. Using a new optimization argument the best values of the parameter are determined. In the case of three numbers the algebraic inequality has some interesting geometric applications involving a generalization of Euler’s inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"50 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010412","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 existence results for a differential equation and an inclusion of fractional order via (convex) F-contraction mapping 微分方程的若干存在性结果以及通过（凸）F-收缩映射的分数阶包容
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-27 DOI: 10.1186/s13660-024-03102-8
Vahid Roomi, Hojjat Afshari, Sabileh Kalantari
{"title":"Some existence results for a differential equation and an inclusion of fractional order via (convex) F-contraction mapping","authors":"Vahid Roomi, Hojjat Afshari, Sabileh Kalantari","doi":"10.1186/s13660-024-03102-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03102-8","url":null,"abstract":"The existence of solutions for a class of μ-Caputo fractional differential equations and an inclusion problem equipped with nonlocal μ-integral boundary conditions are investigated. We use F-contraction, convex F-contraction, and some consequences to achieve the desired goals. Finally, some examples are provided to illustrate the results.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"255 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010409","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
A Pexider system of additive functional equations in Banach algebras 巴拿赫代数中的加法函数方程的 Pexider 系统
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-23 DOI: 10.1186/s13660-024-03104-6
Mehdi Dehghanian, Yamin Sayyari, Siriluk Donganont, Choonkil Park
{"title":"A Pexider system of additive functional equations in Banach algebras","authors":"Mehdi Dehghanian, Yamin Sayyari, Siriluk Donganont, Choonkil Park","doi":"10.1186/s13660-024-03104-6","DOIUrl":"https://doi.org/10.1186/s13660-024-03104-6","url":null,"abstract":"In this paper, we solve the system of functional equations $$begin{aligned} textstylebegin{cases} f(x+y)+g(y-x)=2f(x), g(x+y)-f(y-x)=2g(y) end{cases}displaystyle end{aligned}$$ and we investigate the stability of g-derivations in Banach algebras.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"113 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139947629","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
An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation 决策理论在广义阿波罗尼奥斯型二次函数方程近似中的应用
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-20 DOI: 10.1186/s13660-024-03103-7
Azam Ahadi, Reza Saadati, Tofigh Allahviranloo, Donal O’Regan
{"title":"An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation","authors":"Azam Ahadi, Reza Saadati, Tofigh Allahviranloo, Donal O’Regan","doi":"10.1186/s13660-024-03103-7","DOIUrl":"https://doi.org/10.1186/s13660-024-03103-7","url":null,"abstract":"To make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form $mathrm{diag}(A, B, C)$ (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of $Aast B$ . Using generalized Z-numbers, we define a novel control function to investigate H–U–R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139909867","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
Approximation with Szász-Chlodowsky operators employing general-Appell polynomials 使用通用阿佩尔多项式的 Szász-Chlodowsky 算子近似法
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-20 DOI: 10.1186/s13660-024-03105-5
Nusrat Raza, Manoj Kumar, M. Mursaleen
{"title":"Approximation with Szász-Chlodowsky operators employing general-Appell polynomials","authors":"Nusrat Raza, Manoj Kumar, M. Mursaleen","doi":"10.1186/s13660-024-03105-5","DOIUrl":"https://doi.org/10.1186/s13660-024-03105-5","url":null,"abstract":"This article explores a Chlodowsky-type extension of Szász operators using the general-Appell polynomials. The convergence properties of these operators are established by employing the universal Korovkin-type property, and the order of approximation is determined using the classical modulus of continuity. Additionally, the weighted $mathfrak{B}$ -statistical convergence and statistically weighted $mathfrak{B}$ -summability properties of the operators are derived. Theoretical results are supported by numerical and graphical examples.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139909885","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 integral Jensen inequality 广义积分詹森不等式
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-20 DOI: 10.1186/s13660-024-03106-4
Saeed Nazari Pasari, Ali Barani, Naser Abbasi
{"title":"Generalized integral Jensen inequality","authors":"Saeed Nazari Pasari, Ali Barani, Naser Abbasi","doi":"10.1186/s13660-024-03106-4","DOIUrl":"https://doi.org/10.1186/s13660-024-03106-4","url":null,"abstract":"In this paper we introduce necessary and sufficient conditions for a real-valued function to be preinvex. Some properties of preinvex functions and new versions of Jensen’s integral type inequality in this setting are given. Several examples are also involved.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139909977","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
Approximating fixed points of weak enriched contractions using Kirk’s iteration scheme of higher order 利用柯克高阶迭代方案逼近弱充实收缩的定点
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-14 DOI: 10.1186/s13660-024-03097-2
Mi Zhou, Naeem Saleem, Mujahid Abbas
{"title":"Approximating fixed points of weak enriched contractions using Kirk’s iteration scheme of higher order","authors":"Mi Zhou, Naeem Saleem, Mujahid Abbas","doi":"10.1186/s13660-024-03097-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03097-2","url":null,"abstract":"In this paper, we introduce two types of weak enriched contractions, namely weak enriched $mathcal{F}$ -contraction, weak enriched $mathcal{F^{prime}}$ -contraction, and k-fold averaged mapping based on Kirk’s iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk’s iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"3 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772243","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 fixed points for fuzzy and nonfuzzy mappings in strong b-metric spaces 强 b 矩空间中模糊和非模糊映射的广义定点
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-14 DOI: 10.1186/s13660-024-03101-9
Shazia Kanwal, Hüseyin Işık, Sana Waheed
{"title":"Generalized fixed points for fuzzy and nonfuzzy mappings in strong b-metric spaces","authors":"Shazia Kanwal, Hüseyin Işık, Sana Waheed","doi":"10.1186/s13660-024-03101-9","DOIUrl":"https://doi.org/10.1186/s13660-024-03101-9","url":null,"abstract":"The main purpose of this research article is to generalize Kannan-type fixed-point (FP) theorems for single-valued mappings and Chatterjea-type FP result for fuzzy mappings (FMs) in the context of complete strong b-metric spaces (MSs). Moreover, fuzzy FPs are established for Suzuki-type fuzzy contraction in the setting of complete strong b-MSs. The conclusions are supported by nontrivial examples to enhance the validity of the results obtained in this study. In addition, previous findings have been made as corollaries from the relevant literature. The numerous implications that this technique has across the literature improve and integrate our findings. Applications of some of the results obtained are also incorporated.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"66 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139773377","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
Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold 用修正惯性法解决哈达玛流形中的平衡问题和定点问题的粘度外梯度法
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-02-13 DOI: 10.1186/s13660-024-03099-0
P. V. Ndlovu, L. O. Jolaoso, M. Aphane, H. A. Abass
{"title":"Viscosity extragradient with modified inertial method for solving equilibrium problems and fixed point problem in Hadamard manifold","authors":"P. V. Ndlovu, L. O. Jolaoso, M. Aphane, H. A. Abass","doi":"10.1186/s13660-024-03099-0","DOIUrl":"https://doi.org/10.1186/s13660-024-03099-0","url":null,"abstract":"In this article, we propose a viscosity extragradient algorithm together with an inertial extrapolation method for approximating the solution of pseudomonotone equilibrium and fixed point problem of a nonexpansive mapping in the setting of a Hadamard manifold. We prove that the sequence generated by our iterative method converges to a solution of the above problems under some mild conditions. Finally, we outline some implications of our results and present several numerical examples showing the implementability of our algorithm. The results of this article extend and complement many related results in linear spaces.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139772378","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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