Approximation theorems for total quasi-?-asymptotically nonexpansive mappings with applications

The purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi-?-asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in Banach spaces. In order to get the approximation theorems, the hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article extend and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 134 (2005) 257-266], Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 149 (2007) 103-115], Li, Su [H. Y. Li, Y. F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72(2) (2010) 847-855], Su, Xu and Zhang [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3960], Wang et al. [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. 73 (2010) 2260-2270], Chang et al. [S.S. Chang, C.K. Chan, H.W. Joseph Lee, Modified block iterative algorithm for quasi-?-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput. 217 (2011) 7520-7530], Ofoedu and Malonza [E.U. Ofoedu, D.M. Malonza, Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type, Appl. Math. Comput. 217 (2011) 6019-6030] and Yao et al. [Y.H. Yao, Y.C. Liou, S.M. Kang, Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings, Appl. Math. Comput. 208 (2009) 211-218].     

Strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications

The purpose of this paper is by using the hybrid iterative method to prove some strong convergence theorems for approximating a common element of the set of solutions to a system of generalized mixed equilibrium problems and the set of common fixed points for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su et al. [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], Li and Su [H.Y. Li, Y.F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72 (2) (2010) 847-855], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. TMA 73 (2010) 2260-2270], Kang et al. [J. Kang, Y. Su, X. Zhang, Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications, Nonlinear Anal. HS 4 (4) (2010) 755-765], Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory 134 (2005) 257-266], Tan et al. [J.F. Tan, S.S. Chang, M. Liu, J.I. Liu, Strong convergence theorems of a hybrid projection algorithm for a family of quasi-?-asymptotically nonexpansive mappings, Opuscula Math. 30 (3) (2010) 341-348], Takahashia and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009) 45-57] and Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Systems 3 (2009) 11-20] and others.     

集值映射的对称向量拟均衡问题

研究向量集值映射的拟均衡问题的有效解,利用数值化方法与不动点定理,得到解的存在性定理.作为应用,得到广义向量鞍点,向量变分不等式与向量互补问题的存在性定理.     

DENSITY PROPERTIES OF MAPPING SPACES FOR OPERATOR SPACES

In this article, we give the sufficient and necessary conditions for which several important mapping spaces are weak dense in the corresponding completely bound mapping spaces.     

分担处于一般位置超平面的亚纯映射唯一性定理

本文研究从Cn到复射影空间PN(C)上亚纯映射唯一性问题.根据杨乐处理重值的方法和Dethloff、Quang、Tan等人的技巧,我们分别得到了两个广泛的唯一性定理,改进和推广了一些分担处于一般位置超平面的亚纯映射唯一性结果.     

Noise map validation by continuous noise monitoring

This paper presents a comparison of two noise assessments in the Gdansk agglomeration in Poland. One is based on the noise map produced by computational method for the city in 2007, the second one is based on real data from continuous measurements acquired by a noise monitoring network operating in the city since 2008. Differences are shown and analyzed. Additionally, seasonal and weekday influence on noise indicators (L_DEN, L_D, L_E and L_N) is analyzed and discussed in this paper.     

Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities

A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces.     

Viscosity method for hierarchical fixed point and variational inequalities with applications

A viscosity method for a hierarchical fixed point solving variational inequality problems is presented. The method is used to solve variational inequalities, where the involved mappings are non-expansive. Solutions are sought in the set of the fixed points of another non-expansive mapping. As applications, we use the results to study problems of the monotone variational inequality, the convex programming, the hierarchical minimization, and the quadratic minimization over fixed point sets.     

含非线性摩擦系数的单自由度颤振系统全局动力学行为数值研究

摩擦系数模型取更具普适性的Stribeck非线性模型,基于事件驱动理论,利用C与Matlab联合仿真的方法开发了干摩擦颤振问题的快速求解程序。给出改进的胞映射算法,对含非线性摩擦的单自由度摩擦颤振系统的演化过程及其全局性态进行数值分析和研究,得到系统在任意的初始状态下的响应特性、系统收敛域的数值计算分析结果。分析结果表...     

Site mapping and small molecule blind docking reveal a possible target site on the SARS-CoV-2 main protease dimer interface

The SARS-CoV-2 virus is causing COVID-19 resulting in an ongoing pandemic with serious health, social, and economic implications. Much research is focused in repurposing or identifying new small molecules which may interact with viral or host-cell molecular targets. An important SARS-CoV-2 target is the main protease (M^pro), and the peptidomimetic α-ketoamides represent prototypical experimental inhibitors. The protease is characterised by the dimerization of two monomers each which contains the catalytic dyad defined by Cys¹⁴⁵ and His⁴¹ residues (active site). Dimerization yields the functional homodimer. Here, our aim was to investigate small molecules, including lopinavir and ritonavir, α-ketoamide 13b, and ebselen, for their ability to interact with the M^pro. The sirtuin 1 agonist SRT1720 was also used in our analyses. Blind docking to each monomer individually indicated preferential binding of the ligands in the active site. Site-mapping of the dimeric protease indicated a highly reactive pocket in the dimerization region at the domain III apex. Blind docking consistently indicated a strong preference of ligand binding in domain III, away from the active site. Molecular dynamics simulations indicated that ligands docked both to the active site and in the dimerization region at the apex, formed relatively stable interactions. Overall, our findings do not obviate the superior potency with respect to inhibition of protease activity of covalently-linked inhibitors such as α-ketoamide 13b in the M^pro active site. Nevertheless, along with those from others, our findings highlight the importance of further characterisation of the M^pro active site and any potential allosteric sites.