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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
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- 경남대학교 기초과학연구소 Nonlinear Functional Analysis and Applications Nonlinear Functional Analysis and Applications Vol.25 No.1
- 발행연도
- 2020.1
- 수록면
- 135 - 152 (18page)
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초록· 키워드
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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.
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참고문헌 (25)
참고문헌 신청
M. O. Aibinu / 2018 / The implicit midpoint rule of nonexpansive mappings and applications in uniformly smooth Banach spaces / J. Non-linear Sci. Appl 11:1374~1391
Aibinu Mathew O. / 2019 / CONVERGENCE ANALYSIS OF VISCOSITY IMPLICIT RULES OF NONEXPANSIVE MAPPINGS IN BANACH SPACES / Nonlinear Functional Analysis and Applications 24(4):691~713
M.A. Alghamdi / 2014 / The implicit midpoint rule for nonexpansive mappings / Fixed Point Theory Appl. 2014:96
] V. Berinde / 2004 / Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators / Fixed Point Theory Appl. 2004:2
R.E. Bruck Jr. / 1974 / A strongly convergent iterative solution of 0 ∈ U(x) for a maximal monotone operator U in Hilbert spaces / J. Math. Anal. Appl. 48:114~126
Aibinu Mathew O. / 2019 / CONVERGENCE ANALYSIS OF VISCOSITY IMPLICIT RULES OF NONEXPANSIVE MAPPINGS IN BANACH SPACES / Nonlinear Functional Analysis and Applications 24(4):691~713
M.A. Alghamdi / 2014 / The implicit midpoint rule for nonexpansive mappings / Fixed Point Theory Appl. 2014:96
] V. Berinde / 2004 / Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators / Fixed Point Theory Appl. 2004:2
R.E. Bruck Jr. / 1974 / A strongly convergent iterative solution of 0 ∈ U(x) for a maximal monotone operator U in Hilbert spaces / J. Math. Anal. Appl. 48:114~126
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