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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 81 - 95 (15page)
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초록· 키워드
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Let E be a uniformly convex Banach space with a uniformly Gˆateaux differentiable norm, C a nonempty closed convex subset of E, and T : C -> E a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For f : C -> C a contraction and t in (0; 1), let x_t be a unique fixed point of a contraction T_t : C -> E, defined by T_t x = t f(x) + (1 - t)Tx, x in C. It is proved that if { x_t } is bounded, then x_t converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly Gˆateaux differentiable norm.
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참고문헌 (27)
참고문헌 신청
A. Moudafi / 2000 / Viscosity approximation methods for fixed-points problems / J. Math. Anal. Appl 241 : 46 ~ 55
B. Halpern / 1967 / Fixed points of nonexpansive maps / Bull. Amer. Math. Soc 73 : 957 ~ 961
F. E. Browder / 1967 / Convergence of approximations to fixed points of nonexpansive mappings in Banach spaces / Archs Ration. Mech. Anal 24 : 82 ~ 90
G. E. Kim / 1996 / Strong convergence theorems for nonexpansive nonselfmappings in Banach spaces / Nihonkai Math. J 7 : 63 ~ 72
G. Marino / 1992 / On approximating fixed points for nonexpansive maps / Indian J. Math 34 : 91 ~ 98
B. Halpern / 1967 / Fixed points of nonexpansive maps / Bull. Amer. Math. Soc 73 : 957 ~ 961
F. E. Browder / 1967 / Convergence of approximations to fixed points of nonexpansive mappings in Banach spaces / Archs Ration. Mech. Anal 24 : 82 ~ 90
G. E. Kim / 1996 / Strong convergence theorems for nonexpansive nonselfmappings in Banach spaces / Nihonkai Math. J 7 : 63 ~ 72
G. Marino / 1992 / On approximating fixed points for nonexpansive maps / Indian J. Math 34 : 91 ~ 98
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