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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제29권 제5호
- 발행연도
- 2011.1
- 수록면
- 1,363 - 1,379 (17page)
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Halpern iterative algorithm is one of the most cited in the literature of approximation of fixed points of nonexpansive mappings. Different authors modified this iterative algorithm in Banach spaces to approximate fixed points of nonexpansive mappings. One of which is Hu [8] and Yao et al [21] modification of Halpern iterative algorithm for nonexpansive mappings in Banach spaces. It is the purpose of this paper to thoroughly analyze this modification and its convergence conditions. Unfortunately, Hu [8] and Yao et al [21] control conditions imposed on the modified Halpern iterative algorithm to have strong convergence are found to be not sufficient. In this paper, counterexamples are constructed to prove that the strong convergence conditions of Hu [8] and Yao et al [21] are not sufficient. It is also proved that with some additional conditions on the control parameters, strong convergence of the defined iterative algorithm is obtained in different Banach space settings.
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참고문헌 (22)
참고문헌 신청
H. H. Bauschke / 1996 / The approximation of fixed points of compositions of nonexpansive map-pings in Hilbert space / J. Math. Anal. Appl 202:150~159
F. E. Browder / 1967 / Convergence of approximants to fixed points of nonexpansive maps in Ba-nach spaces / Arch. Rational Mech. Anal 24:82~90
F. E. Browder / 1967 / Convergence theorems for sequences of nonlinear operators in Banach spaces / Mathematische Zeitschrift 100:201~225
F. E. Browder / 1968 / Semicontractive and semiaccretive nonlinear mappings in Banach spaces / Bull. Amer. Math. Soc 74:660~665
S. S. Chang / 1997 / On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces / J. Math. Anal. Appl 216:94~111
F. E. Browder / 1967 / Convergence of approximants to fixed points of nonexpansive maps in Ba-nach spaces / Arch. Rational Mech. Anal 24:82~90
F. E. Browder / 1967 / Convergence theorems for sequences of nonlinear operators in Banach spaces / Mathematische Zeitschrift 100:201~225
F. E. Browder / 1968 / Semicontractive and semiaccretive nonlinear mappings in Banach spaces / Bull. Amer. Math. Soc 74:660~665
S. S. Chang / 1997 / On Chidume's open questions and approximate solutions of multivalued strongly accretive mapping equations in Banach spaces / J. Math. Anal. Appl 216:94~111
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