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Let K be a nonempty closed convex subset of a Banach space
E. Suppose {Tn} (n = 1, 2, . . .) is a uniformly asymptotically regular sequence
of nonexpansive mappings from K to K such that ∩∞n=1 F(Tn) ≠0. For x0 ∈ K, define xn+1 = λn+1xn + (1 − λn+1)Tn+1xn, n ≥ 0. If λn ⊂ [0, 1] satisfies limn→∞ λn = 0, we proved that {xn} weakly converges to some z ∈ F as n → ∞ in the framework of reflexive Banach
space E which satisfies the Opial’s condition or has Fr´echet differentiable
norm or its dual E* has the Kadec-Klee property. We also obtain that {xn} strongly converges to some z ∈ F in Banach space E if K is a compact subset of E or there exists one map T ∈ {Tn; n = 1, 2, . . .} satisfy some compact conditions such as T is semicompact or satisfy Condition A or limn→∞ d(xn, F(T)) = 0 and so on.
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참고문헌 (16)
참고문헌 신청
F. E. Browder / 1968 / Semicontractive and semiaccretive nonlinear mappings in Banach spaces / Bulletin of the American Mathematical Society 74 : 660 ~ 665
H. K. Xu / 1991 / Inequalities in Banach spaces with applications / NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 16 (12) : 1127 ~ 1138
J. G. Falset / 2001 / Weak convergence theorems for asymptotically nonexpansive mappings and semigroups / NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 43 (3) : 377 ~
J. G. O’Hara / 2003 / Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces / NONLINEAR ANALYSIS-THEORY METHODS & APPLIC
J. S. Jung / 2005 / Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces / Journal of Mathematical Analysis and Applications 302 (2) : 509 ~
H. K. Xu / 1991 / Inequalities in Banach spaces with applications / NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 16 (12) : 1127 ~ 1138
J. G. Falset / 2001 / Weak convergence theorems for asymptotically nonexpansive mappings and semigroups / NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 43 (3) : 377 ~
J. G. O’Hara / 2003 / Iterative approaches to finding nearest common fixed points of nonexpansive mappings in Hilbert spaces / NONLINEAR ANALYSIS-THEORY METHODS & APPLIC
J. S. Jung / 2005 / Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces / Journal of Mathematical Analysis and Applications 302 (2) : 509 ~
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