Banach空间中关于Lipschitz φ-半压缩映象的带误差项的Ishikawa迭代过程(英文)

Ishikawa Iterative Process with Errors for Lipschitzian and φ-Hemicontractive Mappings in Banach Spaces

英文关键词:Ishikawa iteration with errors  φ-strongly quasi-accretive mapping  φ-hemicontraction  arbitrary Banach space.

中文摘要:

      本文在任意Ｂａｎａｃｈ空间中研究了Ｌｉｐｓｃｈｉｔｚ φ－半压缩映象与φ－强拟增生映象的带误差项的Ｉｓｈｉｋａｗａ迭代过程，使用新的分析技巧建立了几个强收敛定理．

英文摘要:

      Let X be a real Banish space, K a nonempty convex subset of X such that K + K?K. Let T: K → K be a Lipschitzian andφ-hemicontractive mapping with a Lipschitzian constant L ≥ 1. Let {α_n}^∞_n=0, and {β_n}^∞_n=0 be two real sequences in [0, 1] satisfying: (i) α_n→0,β_n→ 0 as n → ∞; (ii) (?)α_n=∞ . Assume that {u_n}^∞_n=0 and {v_n}^∞_n=0 are two sequences in K satisfying . ‖u_n‖= o(α_n),v_n → 0 as n →∞. For an arbitrary x_n∈K define a sequence {x_n}^∞_n=0 in K by(?) If {Ty_n} is bounded, then the sequence {x_n} converges strongly to the unique fixed point of T. A related result deals with iterative solution of nonlinear equations with φ-strongly quasi-accretive mappings by the Ishikawa iteration with errors in an arbitrary Banach space.