论文信息 - Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space

Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space

Let be a nonempty closed and convex subset of a Hilbert space , let and be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of and defined by , and then prove that converges strongly to a common fixed point of and . The results generalize and unify the corresponding results.

Lei Deng | Jianjun Liu | Lili He

[1] W. Takahashi. Nonlinear Functional Analysis , 2000 .

[2] Wataru Takahashi,et al. Strong Convergence to Common Fixed Points of Families of Nonexpansive Mappings , 1997 .

[3] R. Wittmann. Approximation of fixed points of nonexpansive mappings , 1992 .

[4] Z. Opial. Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[5] W. Takahashi,et al. Strong convergence theorem for asymptotically nonexpansive mappings , 1996 .

[6] J. Baillon. Un theoreme de type ergodique pour les contractions non lineaires dans un espace de Hilbert , 1975 .

[7] Felix E. Browder,et al. Convergence of approximants to fixed points of nonexpansive nonlinear mappings in banach spaces , 1967 .

[8] S Rich. SOME PROBLEMS AND RESULTS IN FIXED POINT THEORY , 1983 .

[9] W. Takahashi,et al. Nonlinear ergodic theorems for nonexpansive mappings in Hilbert spaces , 1979 .