Itrative Approximation of Fixed Points of Uniformly L-Lipschitzian Asymptotically Pseudocontractive Nonself-mappings
Xiang Chang-he · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2009
In 2003,Chidume first introduced the definition of asymptotically nonexpansive nonself-mappings and uniformly L-Lipschitzian nonself-mappings.Furthermore,he proved that the iterative sequence he introduced converged strongly to fixed point of asymptotically nonexpansive nonself-mappings.The definition of asymptotically pseudocontractive nonself-mapping is introduced and the modified Ishikawa iterative sequence {xn} for uniformly L-Lipschitzian asymptotically pseudocontractive nonself-mapping T is presented in this paper.Let K be a retract of a real Banach space E,P be a nonexpansive retraction from E to K.Suppose there exist a strictly increasing function Φ:[0,∞)→[0,∞),Φ(0)=0,Φj(xn+1-x)∈J(xn+1-x)such that 〈T(PT)n-1xn+1-T(PT)n-1x,j(xn+1-x)〉≤kn ‖xn+1-x‖2-Φ(‖xn+1-x‖),n≥1,x is a fixed point of T.This paper proves that the iterative sequence {xn} converges strongly to fixed points x under some restrictive conditions on parameters.The objective of this article is to extend the asymptotically pseudocontractive mappings to asymptotically pseudocontractive nonself-mappings.Therefore,the results presented in this paper extended the previous work.