Pub Date : 2024-03-04DOI: 10.1186/s13660-024-03077-6
Qin Guo, Xianghua Liu, Peixin Ye
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.
我们利用弱重构纯贪婪算法（WRPGA）研究了监督学习中的回归问题。我们应用 WRPGA 构建了学习估计器，并推导出了希尔伯特空间中相应贪婪学习算法的 K 函数误差估计的紧上限。在回归函数的两个先验假设下，得到了令人满意的学习率。与其他贪婪学习算法相比，WRPGA 在监督学习中的应用大大降低了计算成本，同时保持了强大的泛化能力。
{"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}
Pub Date : 2024-03-01DOI: 10.1186/s13660-024-03107-3
Yagub N. Aliyev
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.
{"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}
Pub Date : 2024-02-27DOI: 10.1186/s13660-024-03102-8
Vahid Roomi, Hojjat Afshari, Sabileh Kalantari
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.
{"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}
Pub Date : 2024-02-23DOI: 10.1186/s13660-024-03104-6
Mehdi Dehghanian, Yamin Sayyari, Siriluk Donganont, Choonkil Park
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.
在本文中，我们求解了函数方程组 $$begin{aligned}f(x+y)+g(y-x)=2f(x), g(x+y)-f(y-x)=2g(y) end{cases}displaystyle end{aligned}$$，并研究了巴拿赫代数中 g 衍生的稳定性。
{"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}
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.
为了更好地做出近似决策，我们可能需要增加有关近似不同方面的可靠而有用的信息。为了提高阿波罗尼乌斯型二次函数方程近似解的质量和确定性，我们需要测量近似解的质量和确定性以及最大误差。要衡量其质量，我们使用模糊集；要实现其确定性，我们使用概率分布函数。为了提出上述问题，我们应用了 Z 数的概念，并引入了一个形式为 $mathrm{diag}(A, B, C)$ 的特殊矩阵（命名为广义 Z 数），其中 A 是一个模糊时间戳集合，B 是概率分布函数，C 是 A 的可靠度，用 $Aast B$ 的值来描述。利用广义 Z 数，我们定义了一种新的控制函数来研究 H-U-R 稳定性，以逼近阿波罗尼奥斯型二次函数方程的解，并保证逼近的质量和确定性。
{"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}
Pub Date : 2024-02-20DOI: 10.1186/s13660-024-03105-5
Nusrat Raza, Manoj Kumar, M. Mursaleen
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.
{"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}
Pub Date : 2024-02-20DOI: 10.1186/s13660-024-03106-4
Saeed Nazari Pasari, Ali Barani, Naser Abbasi
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.
{"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}
Pub Date : 2024-02-14DOI: 10.1186/s13660-024-03097-2
Mi Zhou, Naeem Saleem, Mujahid Abbas
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.
本文介绍了两种弱富集收缩，即弱富集 $mathcal{F}$ -收缩、弱富集 $mathcal{F^/{prime}}$ -收缩以及基于 Kirk 阶迭代算法的 k 折平均映射。本文介绍的收缩类型统一、扩展和概括了现有的几类富集和弱富集收缩映射。此外，K 折平均映射可以看作是平均映射和双平均映射的一般化。然后，我们证明了与本文引入的弱富集收缩相关的 K 折平均映射的唯一定点的存在性。我们研究了保证 k 折平均映射和弱充实收缩的定点集相等的必要条件。我们证明，可以使用适当的柯克迭代算法来逼近 k 折平均映射和两个弱充实收缩的定点。我们还研究了 k 折平均映射的好拟性、极限阴影特性和 Ulam-Hyers 稳定性。我们提供了确保每个图示弱增益收缩的周期点性质的必要条件。我们列举了一些例子来说明我们的结果是对现有文献中类似结果的潜在概括。
{"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}
Pub Date : 2024-02-14DOI: 10.1186/s13660-024-03101-9
Shazia Kanwal, Hüseyin Işık, Sana Waheed
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.
{"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}
Pub Date : 2024-02-13DOI: 10.1186/s13660-024-03099-0
P. V. Ndlovu, L. O. Jolaoso, M. Aphane, H. A. Abass
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.
{"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}
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