Iterative Algorithms To Fixed Points Of Self And Nonself-Pseudo-contractions

In this paper we deal with some convergence theorems of classic iterative methods for some pseudo-contractions and nonself pseudo-contractions.In the first chapter, we introduce some revelent definitions, important lemmas and recent results for the pseudo-contraction and the nonself pseudo-contraction.In the second chapter, a kind of double composite modified Ishikawa's iterative sequences of nonexpansive mappings is introduced in the uniformly smooth Banach spaces:u G C is a given point, C is a closed and convex set in the Banach spaces, and {αn},{βn},{γn},{αn},{βn},{γn} are sequences in [0,1].If these sequences satisfy some conditions, we can prove that the sequence{xn} which is defined by (4) converge strongly to the fixed point of T.In the third chapter, We establish a weak convergence theorem of nonself asymp-totically pseudo-contraction by using the modified Mann iteration method in Hilbert spaces: Xn+1=P(αnu+βnxn+γnTxn) (5) We also modify this iteration method by applying projection to get an algorithm by which we get a strong convergence theorem.In the fourth chapter, we establish a weak convergence theorem of nonself asymp-totically strictly pseudo-contraction by using the modified Mann iteration method in Hilbert spaces: We also modify this iteration method by applying projection to get an algorithm by which we get a strong convergence theorem.