ResearchPad - Discrete Mathematics and Combinatorics https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Strong convergence theorems for coordinatewise negatively associated random vectors in Hilbert space]]> https://www.researchpad.co/product?articleinfo=5b589963463d7e4c743d09a6

In this work, some strong convergence theorems are established for weighted sums of coordinatewise negatively associated random vectors in Hilbert spaces. The results obtained in this paper improve and extend the corresponding ones of Huan et al. (Acta Math. Hung. 144(1):132–149, 2014) as well as correct and improve the corresponding one of Ko (J. Inequal. Appl. 2017:290, 2017).

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This paper is devoted to the adaptive Morley element algorithms for a biharmonic eigenvalue problem in [TeX:] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{R}^{n}$\end{document}Rn ([TeX:] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n\geq2$\end{document}n2). We combine the Morley element method with the shifted-inverse iteration including Rayleigh quotient iteration and the inverse iteration with fixed shift to propose multigrid discretization schemes in an adaptive fashion. We establish an inequality on Rayleigh quotient and use it to prove the efficiency of the adaptive algorithms. Numerical experiments show that these algorithms are efficient and can get the optimal convergence rate.

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<![CDATA[Some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions]]> https://www.researchpad.co/product?articleinfo=5bf9c835d5eed0c484411520

The authors obtain some Wilker and Cusa type inequalities for generalized trigonometric and hyperbolic functions and generalize some known inequalities.

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<![CDATA[An approximation theorem and generic convergence for equilibrium problems]]> https://www.researchpad.co/product?articleinfo=5b4ab653463d7e6a020ec1de

In this paper, we prove an approximation theorem for equilibrium problems and provide theoretical support for many algorithms. Simon’s bounded rationality is illustrated by an approximation theorem, that is, bounded rationality is approaching full rationality as its ultimate goal. Furthermore, by the methods of set-valued analysis, we obtain the generic uniqueness and generic convergence of the solutions of monotone equilibrium problems in the sense of Baire category. As applications, we investigate the optimization problem, variational inequality problem and saddle point problem as special cases.

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