Pub Date : 2024-06-05DOI: 10.1186/s13660-024-03148-8
Rakesh K. Parmar, Tibor K. Pogány
We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.
{"title":"Bounds for novel extended beta and hypergeometric functions and related results","authors":"Rakesh K. Parmar, Tibor K. Pogány","doi":"10.1186/s13660-024-03148-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03148-8","url":null,"abstract":"We introduce a new unified extension of the integral form of Euler’s beta function with a MacDonald function in the integrand and establish functional upper bounds for it. We use this definition to extend as well the Gaussian and Kummer’s confluent hypergeometric functions, for which we provide bounding inequalities. Moreover, we use our extension of the beta function to define a new probability distribution, for which we establish raw moments and moment inequalities and, as by-products, Turán inequalities for the initially defined extended beta function.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252710","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 : 2024-06-05DOI: 10.1186/s13660-024-03153-x
Xianghu Liu, Yanfang Li
This study is centered on the optimal controllability of differential equations involving fractional derivatives of Katugampola. We derive both necessary and sufficient conditions for optimal controllability by extending Gronwall’s inequality with singular kernels. Furthermore, we establish conditions ensuring the existence and uniqueness of mild solutions using the Banach fixed-point theorem and the generalized Laplace transform. To underscore the practical relevance of our findings, we provide an illustrative example.
{"title":"On the optimal controllability for a class of Katugampola fractional systems","authors":"Xianghu Liu, Yanfang Li","doi":"10.1186/s13660-024-03153-x","DOIUrl":"https://doi.org/10.1186/s13660-024-03153-x","url":null,"abstract":"This study is centered on the optimal controllability of differential equations involving fractional derivatives of Katugampola. We derive both necessary and sufficient conditions for optimal controllability by extending Gronwall’s inequality with singular kernels. Furthermore, we establish conditions ensuring the existence and uniqueness of mild solutions using the Banach fixed-point theorem and the generalized Laplace transform. To underscore the practical relevance of our findings, we provide an illustrative example.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141252902","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 : 2024-05-29DOI: 10.1186/s13660-024-03091-8
A. I. Saied
In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder’s inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when $mathbb{T}=mathbb{N}$ and $mathbb{T}=mathbb{R}$ ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011).
{"title":"A study on reversed dynamic inequalities of Hilbert-type on time scales nabla calculus","authors":"A. I. Saied","doi":"10.1186/s13660-024-03091-8","DOIUrl":"https://doi.org/10.1186/s13660-024-03091-8","url":null,"abstract":"In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder’s inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when $mathbb{T}=mathbb{N}$ and $mathbb{T}=mathbb{R}$ ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011).","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171043","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 : 2024-05-29DOI: 10.1186/s13660-024-03149-7
Naim L. Braha, Taja Yaying, Mohammad Mursaleen
In this paper, we establish a novel category of sequence spaces $ell _{p}^{q_{lambda}}$ and $ell _{infty}^{q_{lambda}}$ by utlizing q-analogue $Lambda^{q}$ of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with $ell _{p}$ and $ell _{infty}$ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class $(ell _{p}^{q_{lambda}},X)$ of matrices, where X is any of the spaces $ell _{infty }$ , c, or $c_{0}$ . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space $ell _{p}^{q_{lambda}}$ .
{"title":"Sequence spaces derived by (q_{lambda}) operators in (ell _{p}) spaces and their geometric properties","authors":"Naim L. Braha, Taja Yaying, Mohammad Mursaleen","doi":"10.1186/s13660-024-03149-7","DOIUrl":"https://doi.org/10.1186/s13660-024-03149-7","url":null,"abstract":"In this paper, we establish a novel category of sequence spaces $ell _{p}^{q_{lambda}}$ and $ell _{infty}^{q_{lambda}}$ by utlizing q-analogue $Lambda^{q}$ of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with $ell _{p}$ and $ell _{infty}$ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class $(ell _{p}^{q_{lambda}},X)$ of matrices, where X is any of the spaces $ell _{infty }$ , c, or $c_{0}$ . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space $ell _{p}^{q_{lambda}}$ .","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170585","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 : 2024-05-28DOI: 10.1186/s13660-024-03142-0
Ahmad Alhawarat, Zabidin Salleh, Hanan Alolaiyan, Hamid El Hor, Shahrina Ismail
The stationary point of optimization problems can be obtained via conjugate gradient (CG) methods without the second derivative. Many researchers have used this method to solve applications in various fields, such as neural networks and image restoration. In this study, we construct a three-term CG method that fulfills convergence analysis and a descent property. Next, in the second term, we employ a Hestenses-Stiefel CG formula with some restrictions to be positive. The third term includes a negative gradient used as a search direction multiplied by an accelerating expression. We also provide some numerical results collected using a strong Wolfe line search with different sigma values over 166 optimization functions from the CUTEr library. The result shows the proposed approach is far more efficient than alternative prevalent CG methods regarding central processing unit (CPU) time, number of iterations, number of function evaluations, and gradient evaluations. Moreover, we present some applications for the proposed three-term search direction in image restoration, and we compare the results with well-known CG methods with respect to the number of iterations, CPU time, as well as root-mean-square error (RMSE). Finally, we present three applications in regression analysis, image restoration, and electrical engineering.
{"title":"A three-term conjugate gradient descent method with some applications","authors":"Ahmad Alhawarat, Zabidin Salleh, Hanan Alolaiyan, Hamid El Hor, Shahrina Ismail","doi":"10.1186/s13660-024-03142-0","DOIUrl":"https://doi.org/10.1186/s13660-024-03142-0","url":null,"abstract":"The stationary point of optimization problems can be obtained via conjugate gradient (CG) methods without the second derivative. Many researchers have used this method to solve applications in various fields, such as neural networks and image restoration. In this study, we construct a three-term CG method that fulfills convergence analysis and a descent property. Next, in the second term, we employ a Hestenses-Stiefel CG formula with some restrictions to be positive. The third term includes a negative gradient used as a search direction multiplied by an accelerating expression. We also provide some numerical results collected using a strong Wolfe line search with different sigma values over 166 optimization functions from the CUTEr library. The result shows the proposed approach is far more efficient than alternative prevalent CG methods regarding central processing unit (CPU) time, number of iterations, number of function evaluations, and gradient evaluations. Moreover, we present some applications for the proposed three-term search direction in image restoration, and we compare the results with well-known CG methods with respect to the number of iterations, CPU time, as well as root-mean-square error (RMSE). Finally, we present three applications in regression analysis, image restoration, and electrical engineering.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170588","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 : 2024-05-17DOI: 10.1186/s13660-024-03146-w
Awais Rasheed, K. Khan, Josip Pečarić, Ðilda Pečarić
{"title":"Generalizations of Levinson-type inequalities via new Green functions and Hermite interpolating polynomial","authors":"Awais Rasheed, K. Khan, Josip Pečarić, Ðilda Pečarić","doi":"10.1186/s13660-024-03146-w","DOIUrl":"https://doi.org/10.1186/s13660-024-03146-w","url":null,"abstract":"","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140964616","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 : 2024-05-15DOI: 10.1186/s13660-024-03144-y
Kaimin Li, Chaoqian Li
{"title":"Upper bounds for the spectral radius of matrices having the Perron–Frobenius property","authors":"Kaimin Li, Chaoqian Li","doi":"10.1186/s13660-024-03144-y","DOIUrl":"https://doi.org/10.1186/s13660-024-03144-y","url":null,"abstract":"","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140977499","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 : 2024-05-10DOI: 10.1186/s13660-024-03143-z
Graeme Auld, Kritsana Neammanee
In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities $P(S=k)$ when $S=sum_{i=1}^{n}X_{i}$ and $X_{1},X_{2},ldots ,X_{n}$ are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein’s method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case.
在最近的一篇论文中，作者证明了一个关于点概率 $P(S=k)$ 的正态逼近的非均匀局部极限定理，当 $S=sum_{i=1}^{n}X_{i}$ 和 $X_{1},X_{2},ldots ,X_{n}$ 是独立的伯努利随机变量，可能具有不同的成功概率。然而，他们的主要结果包含一个未确定的常数，在一定程度上限制了其适用性。在本文中，我们给出了一个在相同环境下的非均匀约束，但其中有明确的常数。我们的证明使用了斯坦因方法，特别是 K 函数和集中不等式方法。我们还证明了泊松二项随机变量的一个新的均匀局部极限定理，用来帮助简化非均匀情况下的证明。
{"title":"Explicit constants in the nonuniform local limit theorem for Poisson binomial random variables","authors":"Graeme Auld, Kritsana Neammanee","doi":"10.1186/s13660-024-03143-z","DOIUrl":"https://doi.org/10.1186/s13660-024-03143-z","url":null,"abstract":"In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities $P(S=k)$ when $S=sum_{i=1}^{n}X_{i}$ and $X_{1},X_{2},ldots ,X_{n}$ are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein’s method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936825","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 : 2024-05-09DOI: 10.1186/s13660-024-03140-2
Chongyang Liu, Jie Gao, Jeevan Kanesan
The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.
{"title":"Dynamics analysis and optimal control of delayed SEIR model in COVID-19 epidemic","authors":"Chongyang Liu, Jie Gao, Jeevan Kanesan","doi":"10.1186/s13660-024-03140-2","DOIUrl":"https://doi.org/10.1186/s13660-024-03140-2","url":null,"abstract":"The coronavirus disease 2019 (COVID-19) remains serious around the world and causes huge deaths and economic losses. Understanding the transmission dynamics of diseases and providing effective control strategies play important roles in the prevention of epidemic diseases. In this paper, to investigate the effect of delays on the transmission of COVID-19, we propose a delayed SEIR model to describe COVID-19 virus transmission, where two delays indicating the incubation and recovery periods are introduced. For this system, we prove its solutions are nonnegative and ultimately bounded with the nonnegative initial conditions. Furthermore, we calculate the disease-free and endemic equilibrium points and analyze the asymptotical stability and the existence of Hopf bifurcations at these equilibrium points. Then, by taking the weighted sum of the opposite number of recovered individuals at the terminal time, the number of exposed and infected individuals during the time horizon, and the system cost of control measures as the cost function, we present a delay optimal control problem, where two controls represent the social contact and the pharmaceutical intervention. Necessary optimality conditions of this optimal control problem are exploited to characterize the optimal control strategies. Finally, numerical simulations are performed to verify the theoretical analysis of the stability and Hopf bifurcations at the equilibrium points and to illustrate the effectiveness of the obtained optimal strategies in controlling the COVID-19 epidemic.","PeriodicalId":16088,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936886","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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