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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2008.1
- 수록면
- 35 - 43 (9page)
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Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let {T_i}_{i=1}^N be N nonexpansive self-mappings of K with F = ∩^N_{i=1}F(Ti) not= ∅ (here F(Ti) denotes the set of fixed points of Ti). Suppose that one of the mappings in {Ti}^N_{i=1} is semi-compact. Let {a_n} ⊂ [d; 1 − d] for some d ∈ (0; 1) and {b_n} ⊂ [t; 1] for some t ∈ (0; 1]. For arbitrary x_0 ∈ K, let the sequence {x_n} be defined iteratively by
x_n = a_n x_{n−1} + (1 − a_n)T_n y_n;
y_n = b_n x_{n−1} + (1 − b_n)T_n x_n; ∀n ≥ 1;
where T_n = T_n(mod N). Then {x_n} convergence strongly to a common fixed point of the mappings family {T_i}^N_{i=1}.
The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of b_n ≡ 1 or N = 1 are also new.
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참고문헌 (7)
참고문헌 신청
C. E. Chidume / 2003 / Iterative algorithms for nonexpansive mappings and some of their generalizations, Nonlinear Anal. and Appl / Kluwer Academic Publishers : 383 ~ 429
C. E. Chidume / 2005 / Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings / Nonlinear Anal 62 : 1149 ~ 1156
H. K. Xu / 1991 / Inequalities in Banach spaces with applications / Nonlinear Anal 1 : 1127 ~ 1138
H. K. Xu / 2001 / An implicit iterative process for nonexpansive mappings / Numer. Funct. Anal. and Optimiz 22 : 767 ~ 773
K. K Tan / 1993 / Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process / J. Math. Anal. Appl 178 : 301 ~ 308
C. E. Chidume / 2005 / Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings / Nonlinear Anal 62 : 1149 ~ 1156
H. K. Xu / 1991 / Inequalities in Banach spaces with applications / Nonlinear Anal 1 : 1127 ~ 1138
H. K. Xu / 2001 / An implicit iterative process for nonexpansive mappings / Numer. Funct. Anal. and Optimiz 22 : 767 ~ 773
K. K Tan / 1993 / Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process / J. Math. Anal. Appl 178 : 301 ~ 308
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