Pub Date : 2024-03-12DOI: 10.1186/s13660-024-03110-8
Amjad Hussain, Ilyas Khan, Abdullah Mohamed
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.
{"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}
Pub Date : 2024-03-12DOI: 10.1186/s13660-024-03108-2
Hanaa M. Zayed, Teodor Bulboacă
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.
{"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}
Pub Date : 2024-03-07DOI: 10.1186/s13660-023-03062-5
D. Sagheer, S. Batul, A. Daim, A. Saghir, H. Aydi, S. Mansour, W. Kallel
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.
{"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}
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":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}
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":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}
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":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}
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":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}
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":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}
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":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}
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":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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：