In this paper, multiobjective optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.
{"title":"Quasi-Duality Result and Linearization in Multiobjective Quasiconvex Programming","authors":"A. Sadeghieh, Atefeh Hassani Bafrani","doi":"10.30495/JME.V0I0.1657","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1657","url":null,"abstract":"In this paper, multiobjective optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49428872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy’s inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant.
{"title":"Some new extension of Levinson’s integral inequalities","authors":"B. Benaissa","doi":"10.30495/JME.V0I0.1711","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1711","url":null,"abstract":"In 1964, Levinson [4] proved integral inequalities concerning generalization of Hardy’s inequalities. In this paper two results are given. First one is extension of the Levinson Integral inequalities via convexity and the second is for the Levinson Integral inequalities of Hardy, this inequalities are established for p < 1 and some related inequalities are also considered with a sharp constant.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":"15 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41435658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Isoparametric hypersurfaces of Lorentz-Minkowski spaces,classied by M.A. Magid in 1985, is related to the famous family of bi-conservative hypersurfaces. Such a hypersurface has conservative stress-energy with respect to the bienergy functional. A timelike (Lorentzian)hypersurface x : M_1^n ----> E_1^{n+1}, isometrically immersed into the Lorentz-Minkowski space E_1^{n+1} , is said to be biconservative if the tangent com-ponent of vector eld Delta^2 x on M_1^n is identically zero. In this paper,we study on L_k-extension of biconservativity condition. The map L_k on a hypersurface (as the kth extension of Laplace operator L_0 = Delta) is the linearized operator arisen from the rst variation of (k + 1)th mean curvature of hypersurface. After illustrating some examples, we prove that an L_k-biconservative timlike hypersurface of E_1^{n+1}, with atmost two distinct principal curvatures and some additional conditions,is isoparametric.
{"title":"An extended bi-conservativity condition on hypersurfaces of the Minkowski spacetime","authors":"F. Pashaie","doi":"10.30495/JME.V0I0.1760","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1760","url":null,"abstract":"Isoparametric hypersurfaces of Lorentz-Minkowski spaces,classied by M.A. Magid in 1985, is related to the famous family of bi-conservative hypersurfaces. Such a hypersurface has conservative stress-energy with respect to the bienergy functional. A timelike (Lorentzian)hypersurface x : M_1^n ----> E_1^{n+1}, isometrically immersed into the Lorentz-Minkowski space E_1^{n+1} , is said to be biconservative if the tangent com-ponent of vector eld Delta^2 x on M_1^n is identically zero. In this paper,we study on L_k-extension of biconservativity condition. The map L_k on a hypersurface (as the kth extension of Laplace operator L_0 = Delta) is the linearized operator arisen from the rst variation of (k + 1)th mean curvature of hypersurface. After illustrating some examples, we prove that an L_k-biconservative timlike hypersurface of E_1^{n+1}, with atmost two distinct principal curvatures and some additional conditions,is isoparametric.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48496166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
solving optimal control problems (OCP) with analytical methods has usually been difficult or not cost-effective. Therefore, solving these problems requires numerical methods. There are, of course, many ways to solve these problems. One of the methods available to solve OCP is a forward-backward sweep method (FBSM). In this method, the state variable is solved in a forward and co-state variable by a backward method where an explicit Runge--Kutta method (ERK) is often used to solve differential equations arising from OCP.In this paper, instead of the ERK method, two hybrid methods based on ERK method of order 3 and 4 are proposed for the numerical approximation of the OCP. Truncation errors and stability analysis of the presented methods are illustrated. Finally, numerical results of the five optimal control problems obtained by new methods, which shows that new methods give us more accurate results, are compared with those of ERK methods of orders 3 and 4 for solving OCP.
{"title":"FBSM Solution of Optimal Control Problems using Hybrid Runge-Kutta based Methods","authors":"M. Ebadi, A. Haghighi, I. Maleki, A. Ebadian","doi":"10.30495/JME.V0I0.1641","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1641","url":null,"abstract":"solving optimal control problems (OCP) with analytical methods has usually been difficult or not cost-effective. Therefore, solving these problems requires numerical methods. There are, of course, many ways to solve these problems. One of the methods available to solve OCP is a forward-backward sweep method (FBSM). In this method, the state variable is solved in a forward and co-state variable by a backward method where an explicit Runge--Kutta method (ERK) is often used to solve differential equations arising from OCP.In this paper, instead of the ERK method, two hybrid methods based on ERK method of order 3 and 4 are proposed for the numerical approximation of the OCP. Truncation errors and stability analysis of the presented methods are illustrated. Finally, numerical results of the five optimal control problems obtained by new methods, which shows that new methods give us more accurate results, are compared with those of ERK methods of orders 3 and 4 for solving OCP.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44413239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, the solution of fuzzy Bernoulli differential equation (FBDE) of the form u'(t)+p(t) u(t)=q(t) u^n(t), u(0)=u0, is investigated in which p(t) and q(t) are real continues functions, u(t)=(x(t),y(t),z(t)) is LR fuzzy function, u0 is LR fuzzy number . First, n th power of LR fuzzy number is defined then using generalized Hukuhara difference and differentiability, [i.gH]-differentiability and [ii.gH]-differentiability are described. Thereafter, by solving 1-cut FBDE, determining the sign of x(t), p(t), q(t) and defining a theorem, u(t) as a LR fuzzy function is calculated. Finally, numerical examples verify the effectiveness of the proposed method.
{"title":"A New Method for Solving Fuzzy Bernoulli Differential Equation","authors":"F. Babakordi, T. Allahviranloo","doi":"10.30495/JME.V0I0.1704","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1704","url":null,"abstract":"Abstract In this paper, the solution of fuzzy Bernoulli differential equation (FBDE) of the form u'(t)+p(t) u(t)=q(t) u^n(t), u(0)=u0, is investigated in which p(t) and q(t) are real continues functions, u(t)=(x(t),y(t),z(t)) is LR fuzzy function, u0 is LR fuzzy number . First, n th power of LR fuzzy number is defined then using generalized Hukuhara difference and differentiability, [i.gH]-differentiability and [ii.gH]-differentiability are described. Thereafter, by solving 1-cut FBDE, determining the sign of x(t), p(t), q(t) and defining a theorem, u(t) as a LR fuzzy function is calculated. Finally, numerical examples verify the effectiveness of the proposed method.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46429464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.
{"title":"Specific Complete Measure in the Structure of a Utility Function","authors":"S. Mohammadzadeh","doi":"10.30495/JME.V0I0.1578","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1578","url":null,"abstract":"An outer measure is constructed on a pseudo-ordered set(X,≿) and then it will be shown that it is in fact a measure defined onthe whole power set of X . Applying this, a measurable utility functionθ is defined which represents the relation ≿ on X. Also, we discuss thecontinuity and upper semi-continuity of θ in certain points of X. Finally,the results are used to improve some of the theorems in economics.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45733045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It is well known that bias in parameter estimates arises when there are measurement errors in the covariates of regression mod- els. One solution for decreasing such biases is the use of prior informa- tion concerning the measurement error, which is often called replication data. In this paper, we present a ridge estimator in replicated measure- ment error (RMER) to overcome the multicollinearity problem in such models. The performance of RMER against some other estimators is investigated. Large sample properties of our estimator are derived and compared with other estimators using a simulation study as well as a real data set.
{"title":"Performance of Ridge Regression Approach in Linear Measurement Error Models with Replicated Data","authors":"Abdol Rasoul Ziaei, K. Zare, Ayoub Sheikhi","doi":"10.30495/JME.V0I0.1581","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1581","url":null,"abstract":"It is well known that bias in parameter estimates arises when there are measurement errors in the covariates of regression mod- els. One solution for decreasing such biases is the use of prior informa- tion concerning the measurement error, which is often called replication data. In this paper, we present a ridge estimator in replicated measure- ment error (RMER) to overcome the multicollinearity problem in such models. The performance of RMER against some other estimators is investigated. Large sample properties of our estimator are derived and compared with other estimators using a simulation study as well as a real data set.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43584972","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. B. K. Balgeshir, S. Uddin, Soghra Tarigi Ahmadsaryi
In this paper, we study hemi-slant submanifolds of 3-Sasakian manifolds. First, we obtain some new results in terms of the operators $T_i$ and $n_i$ and then by using Gauss, Codazzi and Ricci equations, we prove some results involving Ricci and scalar curvature tensors in terms of the slant angle and the mean curvature vector of the submanifold.
{"title":"Ricci and scalar curvatures of hemi-slant submanifolds in 3-Sasakian space forms","authors":"M. B. K. Balgeshir, S. Uddin, Soghra Tarigi Ahmadsaryi","doi":"10.30495/JME.V0I0.1677","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1677","url":null,"abstract":"In this paper, we study hemi-slant submanifolds of 3-Sasakian manifolds. First, we obtain some new results in terms of the operators $T_i$ and $n_i$ and then by using Gauss, Codazzi and Ricci equations, we prove some results involving Ricci and scalar curvature tensors in terms of the slant angle and the mean curvature vector of the submanifold.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41901423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this note, we consider fractional Strum-Liouville boundary value problem containing Caputo derivative of order $alpha$, $ 1
在本文中，我们考虑了含有阶为$alpha$，$1
{"title":"A note on Lyapunov-type inequalities for fractional boundary value problems with Sturm-Liouville boundary conditions","authors":"Anil Chavada, Nimisha Pathak","doi":"10.30495/JME.V0I0.1634","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1634","url":null,"abstract":"In this note, we consider fractional Strum-Liouville boundary value problem containing Caputo derivative of order $alpha$, $ 1<alphaleq 2$ with mixed boundary conditions. We establish Cauchy-Schwarz-type inequality to determine a lower bound for the smallest eigenvalues. We give comparison between the smallest eigenvalues and its lower bounds obtained from the Lyapunov-type and Cauchy-Schwarz-type inequalities. Result shows that the Lyapunov-type inequality gives the worse and Cauchy-Schwarz-type inequality gives better lower bound estimates for the smallest eigenvalues. We then use these inequalities to obtain an interval where a linear combination of certain Mittag-Leffler functions have no real zeros.","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43964545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the idea of S^{JS}- metric spaces which is a generalization of metric spaces. We next study the properties of S^{JS}- metric spaces and prove several theorems. We also deal with abstract S^{JS}- topological spaces induced by S^{JS}- metric and obtain several classical results including Cantor's intersection theorem in this setting. DOI: 10.1735/jme.2021.01.01134
{"title":"S^{JS}- metric and topological spaces","authors":"Ismat Beg, K. Roy, M. Saha","doi":"10.30495/JME.V0I0.1589","DOIUrl":"https://doi.org/10.30495/JME.V0I0.1589","url":null,"abstract":"We introduce the idea of S^{JS}- metric spaces which is a generalization of metric spaces. We next study the properties of S^{JS}- metric spaces and prove several theorems. We also deal with abstract S^{JS}- topological spaces induced by S^{JS}- metric and obtain several classical results including Cantor's intersection theorem in this setting. DOI: 10.1735/jme.2021.01.01134","PeriodicalId":43745,"journal":{"name":"Journal of Mathematical Extension","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43686752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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