http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
CONVERGENCE ANALYSIS OF VISCOSITY IMPLICIT RULES OF NONEXPANSIVE MAPPINGS IN BANACH SPACES
Aibinu Mathew O.,Kim Jong Kyu 경남대학교 기초과학연구소 2019 Nonlinear Functional Analysis and Applications Vol.24 No.4
In this paper, the study of implicit viscosity approximation methods for non-expansive mappings in Banach spaces is explored. A new iterative sequence is introduced for the class of nonexpansive mappings in Banach spaces. Suitable conditions are imposed on the control parameters to prove a strong convergence theorem. Moreover, the strong convergence of the newly introduced sequence to a xed point of a nonexpansive mapping is obtained which also solves the variational inequality problem. These results are improvement and extension of some recent corresponding results announced.
ON THE RATE OF CONVERGENCE OF VISCOSITY IMPLICIT ITERATIVE ALGORITHMS
Mathew O. Aibinu,Jong Kyu Kim 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.1
An essential numerical method for solving ordinary differential and differential algebraic equations is the implicit midpoint rule. Comparing the rate of convergence of the implicit midpoint rules by using numerical examples is common in the literatures. Under suitable conditions imposed on the control parameters, it is shown in this paper that certain two implicit iterative sequences converge to the same fixed point of a nonexpansive mapping in uniformly smooth Banach spaces. Moreover, analytical comparison for the rate of convergence of the implicit iterative sequences to a fixed point of a nonexpansive mapping in uniformly smooth Banach spaces is presented. The implicit iterative sequence which converges faster is determined by an analytical method which is more general than the numerical methods.