渐近φ-半压缩映象不动点的Ishikawa迭代逼近

Iterative Approximative of Fixed Points for Asymptotically φ-hemicontractive Mappings

研究在任意Banach空间中,用修改的Ishikawa迭代序列逼近一致L-Lipschitz的渐近φ-半压缩映象T的不动点问题,在条件limn→∞αn=0,lni→m∞βn=0,∑∞n=0αn=+∞下,给出了迭代序列{xn}强收敛于T的不动点q的充分必要条件.T的修改的Mann迭代序列作为Ishikawa迭代序列的特殊情况,可得到相应的结果.

Fixed points with uniformly L-Lipschitz asymptotically φ-hemicontractive mapping by the modified Ishikawa iterative sequences in the Banach space, and under the conditions of lim n→∞ αn=0,lim n→∞ βn=0,∑ ∞ n=0 αn=＋∞ are discussed. The necessary and sufficient conditions for the iterative sequences {Xn} strong converge to a fixed point are also given.