For a polynomial p(z) = an ∏n t=1(z − zt) of degree n having all its zeros in |z| ≤ K, K ≥ 1 it is known that max |z|=1 |p′(z)| ≥ 2 1 + Kn { n ∑ t=1 K K + |zt| } max |z|=1 |p(z)| . By assuming a possible zero of order m, 0 ≤ m ≤ n− 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.
For a polynomial p (z) = an∏n t−z = 1 (zt)学位的n z玩得都是它的墙在| |≤K, K≥1是知道那个麦克斯| | z = 1′| p (z) | Kn {n≥2 1 +∑t = 1 K K + | zt |}麦克斯| | z = 1 | p (z) |。由assuming秩序之a可能是0,0≤m≤n−4的at, z = 0,则p (z)为n≥k + m + 1与整数k≥3我们有获得a new refinement认识之论点。
{"title":"On the Derivative of a Polynomial with Prescribed Zeros","authors":"V. K. Jain","doi":"10.7862/RF.2017.7","DOIUrl":"https://doi.org/10.7862/RF.2017.7","url":null,"abstract":"For a polynomial p(z) = an ∏n t=1(z − zt) of degree n having all its zeros in |z| ≤ K, K ≥ 1 it is known that max |z|=1 |p′(z)| ≥ 2 1 + Kn { n ∑ t=1 K K + |zt| } max |z|=1 |p(z)| . By assuming a possible zero of order m, 0 ≤ m ≤ n− 4, at z = 0, of p(z) for n ≥ k + m + 1 with integer k ≥ 3 we have obtained a new refinement of the known result.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123365596","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}
{"title":"Maximal ideal space of certain alpha-Lipschitz operator algebras","authors":"A. Shokri, A. Shokri","doi":"10.7862/RF.2012.7","DOIUrl":"https://doi.org/10.7862/RF.2012.7","url":null,"abstract":"","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126282851","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 paper we introduce some multiplier sequence spaces of fuzzy numbers by using a Musielak-Orlicz functionM = (Mk) and multiplier function u = (uk) and prove some inclusion relations between the resulting sequence spaces. AMS Subject Classification: 40A05, 40D25
{"title":"Multiplier sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function","authors":"K. Raj, Amit Gupta","doi":"10.7862/RF.2012.6","DOIUrl":"https://doi.org/10.7862/RF.2012.6","url":null,"abstract":"In this paper we introduce some multiplier sequence spaces of fuzzy numbers by using a Musielak-Orlicz functionM = (Mk) and multiplier function u = (uk) and prove some inclusion relations between the resulting sequence spaces. AMS Subject Classification: 40A05, 40D25","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125912449","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 paper, we introduce the notions of generalised quasi-ideals and generalised bi-ideals in a ternary semigroup. We also characterised these notions in terms of minimal quasi-ideals and minimal bi-ideals in a ternary semigroup. AMS Subject Classification: 16Y30, 16Y60
{"title":"On Generalised Quasi-ideals and Bi-ideals in Ternary Semigroups","authors":"M. K. Dubey, R. Anuradha","doi":"10.7862/RF.2014.3","DOIUrl":"https://doi.org/10.7862/RF.2014.3","url":null,"abstract":"In this paper, we introduce the notions of generalised quasi-ideals and generalised bi-ideals in a ternary semigroup. We also characterised these notions in terms of minimal quasi-ideals and minimal bi-ideals in a ternary semigroup. AMS Subject Classification: 16Y30, 16Y60","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116871328","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 paper we present an extension of the nonconformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractional case. AMS Subject Classification: 26B12, 26A24, 35S05.
{"title":"Towards a Non-conformable Fractional Calculus of n-Variables","authors":"F. Martínez, J. E. Nápoles","doi":"10.7862/rf.2020.6","DOIUrl":"https://doi.org/10.7862/rf.2020.6","url":null,"abstract":"In this paper we present an extension of the nonconformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractional case. AMS Subject Classification: 26B12, 26A24, 35S05.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124454275","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}
A. Abbas, M. Benchohra, Prof. Dr. Mohamed Abdalla Darwish
In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain. AMS Subject Classification: 26A33, 34G20, 34A40, 45N05, 47H10.
{"title":"Some New Existence Results and Stability Concepts for Fractional Partial Random Differential Equations","authors":"A. Abbas, M. Benchohra, Prof. Dr. Mohamed Abdalla Darwish","doi":"10.7862/rf.2016.1","DOIUrl":"https://doi.org/10.7862/rf.2016.1","url":null,"abstract":"In the present paper we provide some existence results and Ulam’s type stability concepts for the Darboux problem of partial fractional random differential equations in Banach spaces, by applying the measure of noncompactness and a random fixed point theorem with stochastic domain. AMS Subject Classification: 26A33, 34G20, 34A40, 45N05, 47H10.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132720786","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: Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4 T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of CD4 T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.
{"title":"Application of the multi-step differential transform method to solve a fractional human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells","authors":"M. Zurigat, M. Ababneh","doi":"10.7862/RF.2015.13","DOIUrl":"https://doi.org/10.7862/RF.2015.13","url":null,"abstract":"Abstract: Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4 T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of CD4 T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131922702","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 paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach. AMS Subject Classification: 45G10, 47H08, 47H10.
{"title":"Measures of Noncompactness in a Banach Algebra and Their Applications","authors":"S. Dudek","doi":"10.7862/RF.2017.5","DOIUrl":"https://doi.org/10.7862/RF.2017.5","url":null,"abstract":"In this paper we study the existence of solutions of a nonlinear quadratic integral equation of fractional order. This equation is considered in the Banach space of real functions defined, continuous and bounded on the real half axis. Additionally, using the technique of measures of noncompactness we obtain some characterization of considered integral equation. We provide also an example illustrating the applicability of our approach. AMS Subject Classification: 45G10, 47H08, 47H10.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127745250","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}
A problem of simultaneously reducing a group of interval uncertainties is considered. The intervals are positively normalized. There is a constraint, by which the sum of any point estimates taken from those intervals is equal to 1. Hence, the last interval is suspended. For mapping the interval uncertainties into point estimates, a minimax decision-making method is suggested. The last interval’s point estimate is then tacitly found. Minimax is applied to a maximal disbalance between a real unknown amount and a guessed amount. These amounts are interpreted as aftermaths of the point estimation. According to this model, the decision-maker is granted a pure strategy, whose components are the most appropriate point estimates. Such strategy is always single. Its components are always less than the right endpoints. The best mapping case is when we obtain a totally regular strategy whose components are greater than the left endpoints. The irregular strategy’s components admitting many left endpoints are computed by special formulae. The worst strategy exists, whose single component is greater than the corresponding left endpoint. Apart from the point estimation, irregularities in the decision-maker’s optimal strategy may serve as an evidence of the intervals’ incorrectness. The irregularity of higher ranks is a criterion for correcting the intervals. AMS Subject Classification: 91A05, 91A35, 90C47.
{"title":"A Minimax Approach to Mapping Partial Interval Uncertainties into Point Estimates","authors":"V. Romanuke","doi":"10.7862/rf.2019.10","DOIUrl":"https://doi.org/10.7862/rf.2019.10","url":null,"abstract":"A problem of simultaneously reducing a group of interval uncertainties is considered. The intervals are positively normalized. There is a constraint, by which the sum of any point estimates taken from those intervals is equal to 1. Hence, the last interval is suspended. For mapping the interval uncertainties into point estimates, a minimax decision-making method is suggested. The last interval’s point estimate is then tacitly found. Minimax is applied to a maximal disbalance between a real unknown amount and a guessed amount. These amounts are interpreted as aftermaths of the point estimation. According to this model, the decision-maker is granted a pure strategy, whose components are the most appropriate point estimates. Such strategy is always single. Its components are always less than the right endpoints. The best mapping case is when we obtain a totally regular strategy whose components are greater than the left endpoints. The irregular strategy’s components admitting many left endpoints are computed by special formulae. The worst strategy exists, whose single component is greater than the corresponding left endpoint. Apart from the point estimation, irregularities in the decision-maker’s optimal strategy may serve as an evidence of the intervals’ incorrectness. The irregularity of higher ranks is a criterion for correcting the intervals. AMS Subject Classification: 91A05, 91A35, 90C47.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"116 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122614587","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 decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : M → E is said to be biharmonic if ∆x = 0, where ∆ is the Laplace operator. We study the Lr-biharmonic hypersurfaces as a generalization of biharmonic ones, where Lr is the linearized operator of the (r + 1)th mean curvature of the hypersurface and in special case we have L0 = ∆. We prove that Lr-biharmonic hypersurface of Lr-finite type and also Lr-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.
{"title":"On some Lr-biharmonic Euclidean Hypersurfaces","authors":"A. Mohammadpouri, F. Pashaie","doi":"10.7862/RF.2016.7","DOIUrl":"https://doi.org/10.7862/RF.2016.7","url":null,"abstract":"In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : M → E is said to be biharmonic if ∆x = 0, where ∆ is the Laplace operator. We study the Lr-biharmonic hypersurfaces as a generalization of biharmonic ones, where Lr is the linearized operator of the (r + 1)th mean curvature of the hypersurface and in special case we have L0 = ∆. We prove that Lr-biharmonic hypersurface of Lr-finite type and also Lr-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.","PeriodicalId":345762,"journal":{"name":"Journal of Mathematics and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123917015","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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