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Ahmed Al-Rawashdeh 《Numerical Functional Analysis & Optimization》2019,40(3):326-340
The concept of quasi-nonexpansive mappings was initiated in Diaz and Metcalf (Bull. Amer. Math. Soc. 73 (1967), 516–519), further it was generalized by Petryshyn and Williamson (Journal of Mathematical Analysis and Applications 43, no. 2 (1973): 459-497). Further investigating the above work, in this article a Banach space with a relation ρ has been considered, the notion of ρ-preserving and quasi ρ-preserving locally related quasi-nonexpansive mappings has been introduced. It has been shown that every ρ-preserving mapping is a quasi ρ-preserving and every nonexpansive mapping is locally related quasi-nonexpansive but converse may not hold. The necessary and sufficient conditions for the convergence of Picard, Mann and Ishikawa iterations of ρ-preserving, quasi ρ-preserving locally related quasi-nonexpansive mappings are presented. 相似文献
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Firoz Firozzaman Fahim Firoz 《International Journal of Mathematical Education in Science & Technology》2017,48(5):756-762
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the given conditions, one may need to understand the concept of modulo arithmetic in number theory. The Chinese Remainder Theorem is a known method to solve these types of problems using modulo arithmetic. In this paper, an efficient remainder rule has been proposed based on basic mathematical concepts. These core concepts are as follows: basic remainder rules of divisions, linear equation in slope intercept form, arithmetic progression and the use of a graphing calculator. These are easily understood by students who have taken prealgebra or intermediate algebra. 相似文献
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In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △? convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature. 相似文献
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This note is denoted to establishing sharp distortion theorems for subclasses of α-Bloch mappings defined in the unit ball of Cn with critical points.Furthermore,the estimates of Bloch constant with respect to these subclasses are given. 相似文献
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In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B n respectively. 相似文献
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When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H ∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H ∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part (Ⅰ)of the paper. The modal synthesis method for computation of the optimal H ∞ norm of decentralized control systems and numerical examples are presented in part (Ⅱ). 相似文献
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任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法 总被引:1,自引:0,他引:1
采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。 相似文献