Strong convergence of Reich-Takahashi iterative sequence for asymptotically pseudo-contractive mapping;

Strong convergence of some iterative sequences for asymptotically nonexpansive mappings in Banach spances;

Aim\ The convergence of Mann iterative sequences of real functions defined on unbounded convex domain is discussed.

For a lot of nonlinear mappings,the fixed points can be approximated by iteration sequence {xn}.

Convergence of Ishikawa iteration sequence for setvalued nonexpansive mapping are discussed in uniformly covex Banach space, and the conditions are shown which guarantee the convergence of the iteration sequence to a fixed point.

This article will set up an iteration sequence and extent its results to a more comprehensive mapping-semi-compact 1-set mapping.

The convergences of three kinds of iterations(modified Mann iterations,modified Ishikawa iterations and modified three-step iterations)are equivalent,if T is a strongly successively pseudocontractive.

By properties of a new analytical method, it proves that the three-step iterative set sequence with (random) errors converges strongly to the fixed point set of a multivalued asymptotically Φ-hemicontractive type mappings in an arbitrary Banach spaces.