New iterations with errors for approximating common fixed points for two generalized asymptotically quasi-nonexpansive nonself-mappings

作者：Thianwan S^*

来源：Mathematical Notes, 2011, 89(3-4): 397-407.

DOI：10.1134/S0001434611030114

• asymptotically quasi-nonexpansive non-self-mapping
• normed linear space
• uniformly L-Lipschitzian mapping
• strong convergence
• common fixed points

Let X be a real uniformly convex Banach space and C a nonempty closed convex nonexpansive retract of X with P as a nonexpansive retraction. Let T (1), T (2): C -> X be two uniformly L-Lipschitzian, generalized asymptotically quasi-nonexpansive non-self-mappings of C satisfying condition A' with sequences {k (n) ((i)) } and {delta (n) ((i)) } aS, [1, a),, i = 1, 2, respectively such that I pound (n=1) (a) (k (n) ((i)) - 1) < a, I pound (n=1) ((i)) delta (n) ((i)) < a, and F = F(T (1)) a (c) F(T (2)) not equal a.... For an arbitrary x (1) a C, let {x (n) } be the sequence in C defined by y(n) = P((1-beta(n) - gamma(n))x(n) + beta(n) T(2)(PT(2))(n-1) x(n) + gamma(n)u(n)), x(n+1) = P ((1-alpha(n) - lambda(n))y(n) broken vertical bar alpha(n)T(1) (PT(1))(n-1) x(n) broken vertical bar lambda(n)u(n)), n >= 1, where {alpha (n) }, {beta (n) }, {gamma (n) } and {lambda (n) } are appropriate real sequences in [0, 1) such that I pound (n=1) (a) ] gamma (n) < a, I pound (n=1) (a) lambda (n) < a, and {u (n) }, }v (n) } are bounded sequences in C. Then {x (n) } and {y (n) } converge strongly to a common fixed point of T (1) and T (2) under suitable conditions.

• 出版日期2011-4