On iterations for families of asymptotically pseudocontractive mappings

Strong convergence of approximated iterations for asymptotically pseudocontractive mappings

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...

Strong convergence of two finite families of asymptotically pseudocontractive mappings

In this paper, we propose a modified implicit iteration for two finite families of asymptotically pseudocontractive mappings. Further, convergence theorems for approximation of common fixed points of two finite families of uniformly Lipschitzian asymptotically pseudocontractive mappings are proved in Banach spaces. Our results extend and improve a number of results in the literature. We also re...

Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings

On modified Noor iterations for strongly pseudocontractive mappings

In this paper, we analyze a three-step iterative scheme for three strongly pseudocontractive mappings in a uniformly smooth Banach space. Our results can be viewed as an extension of three-step and two-step iterative schemes of Glowinski and Le Tallec [3], Noor [1215] and Ishikawa [7], Liu [10] and Xu [20]. 2000 Mathematics Subject Classification: Primary 47H10, 47H17: Secondary 54H25

Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities

and Applied Analysis 3 limn→∞tn 1, ∑∞ n 1 tn 1 − tn ∞, and limn→∞ kn − 1 / kn − tn 0, where ξn min{ 1 − α kn/ kn − α , 1/kn}. For an arbitrary z0 ∈ K let the sequence {zn} be iteratively defined by zn 1 ( 1 − tn kn ) f zn tn kn Tzn, n ∈ N. 1.7 Then i for each integer n ≥ 0, there is a unique xn ∈ K such that xn ( 1 − tn kn ) f xn tn kn Txn; 1.8