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Variable Herz–Morrey estimates for rough fractional Hausdorff operator 粗糙分数 Hausdorff 算子的可变 Herz-Morrey 估计数
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-03-12 DOI: 10.1186/s13660-024-03110-8
Amjad Hussain, Ilyas Khan, Abdullah Mohamed
{"title":"Variable Herz–Morrey estimates for rough fractional Hausdorff operator","authors":"Amjad Hussain, Ilyas Khan, Abdullah Mohamed","doi":"10.1186/s13660-024-03110-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03110-8","url":null,"abstract":"As a first attempt, we obtain the boundedness of the rough fractional Hausdorff operator on variable exponent Herz-type spaces. The method used in this paper enables us to study the operator on some other function spaces with variable exponents.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126801","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
Geometric characterization of the generalized Lommel–Wright function in the open unit disc 开放单位圆盘中广义洛梅尔-赖特函数的几何特征
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-03-12 DOI: 10.1186/s13660-024-03108-2
Hanaa M. Zayed, Teodor Bulboacă
{"title":"Geometric characterization of the generalized Lommel–Wright function in the open unit disc","authors":"Hanaa M. Zayed, Teodor Bulboacă","doi":"10.1186/s13660-024-03108-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03108-2","url":null,"abstract":"The present investigation aims to examine the geometric properties of the normalized form of the combination of generalized Lommel–Wright function $mathfrak{J}_{lambda ,mu}^{nu ,m}(z):=Gamma ^{m}(lambda +1) Gamma (lambda +mu +1)2^{2lambda +mu}z^{1-(nu /2)-lambda} mathcal{J}_{lambda ,mu }^{nu ,m}(sqrt{z})$ , where the function $mathcal{J}_{lambda ,mu}^{nu ,m}$ satisfies the differential equation $mathcal{J}_{lambda ,mu}^{nu ,m}(z):=(1-2lambda -nu )J_{ lambda ,mu}^{nu ,m}(z)+z (J_{lambda ,mu }^{nu ,m}(z) )^{prime}$ with $$ J_{nu ,lambda}^{mu ,m}(z)= biggl(frac{z}{2} biggr)^{2lambda + nu} sum_{k=0}^{infty} frac{(-1)^{k}}{Gamma ^{m} (k+lambda +1 )Gamma (kmu +nu +lambda +1 )} biggl(frac{z}{ 2} biggr)^{2k} $$ for $lambda in mathbb{C}setminus mathbb{Z}^{-}$ , $mathbb{Z}^{-}:= { -1,-2,-3,ldots }$ , $min mathbb{N}$ , $nu in mathbb{C}$ , and $mu in mathbb{N}_{0}:=mathbb{N}cup {0}$ . In particular, we employ a new procedure using mathematical induction, as well as an estimate for the upper and lower bounds for the gamma function inspired by Li and Chen (J. Inequal. Pure Appl. Math. 8(1):28, 2007), to evaluate the starlikeness and convexity of order α, $0leq alpha <1$ . Ultimately, we discuss the starlikeness and convexity of order zero for $mathfrak{J}_{lambda ,mu} ^{nu ,m}$ , and it turns out that they are useful to extend the range of validity for the parameter λ to $lambda geq 0$ where the main concept of the proofs comes from some technical manipulations given by Mocanu (Libertas Math. 13:27–40, 1993). Our results improve, complement, and generalize some well-known (nonsharp) estimates.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126730","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
Well-posed fixed point results and data dependence problems in controlled metric spaces 受控度量空间中的好算定点结果和数据依赖问题
IF 1.6 3区 数学
Journal of Inequalities and Applications Pub Date : 2024-03-07 DOI: 10.1186/s13660-023-03062-5
D. Sagheer, S. Batul, A. Daim, A. Saghir, H. Aydi, S. Mansour, W. Kallel
{"title":"Well-posed fixed point results and data dependence problems in controlled metric spaces","authors":"D. Sagheer, S. Batul, A. Daim, A. Saghir, H. Aydi, S. Mansour, W. Kallel","doi":"10.1186/s13660-023-03062-5","DOIUrl":"https://doi.org/10.1186/s13660-023-03062-5","url":null,"abstract":"The present research is aimed to analyze the existence of strict fixed points (SFPs) and fixed points of multivalued generalized contractions on the platform of controlled metric spaces (CMSs). Wardowski-type multivalued nonlinear operators have been introduced employing auxiliary functions, modifying a new contractive requirement form. Well-posedness of obtained fixed point results is also established. Moreover, data dependence result for fixed points is provided. Some supporting examples are also available for better perception. Many existing results in the literature are particular cases of the results established.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140054666","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
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