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

In this paper we deal with some strong convergence theorems of sev-eral iterative sequences for some strict pseudo-contraction and strict non-self pseudo-contraction.In the first chapter, we introduce some revelent definitions, important lemmas and recent results for some strict pseudo-contraction and strict nonself pseudo-contraction.In the second chapter, a modified of composite Halpern's three-step iterative scheme of nonexpansive mapping is introduced in the uniformly smooth Banach space: where{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 (1) converges strongly to the fixed point of T.In the third chapter, a new three-step iterative scheme ofκ-strict non- self pseudo-contraction mapping is introduced in Hilbert space: where.{αn},{βn},{γn},{μn},{δn},{λn}are sequences in(0,1).If these sequences satisfy some certain conditions,we can prove that the sequence {xn) which is defined by(2)converges strongly t0 the fixed point of T.In the fourth chapter,an iterative scheme for a finite family ofκi-strict nonself pseudo-contraction mappings is introduced in a real q-uniformly smooth and strictly convex Banach space: where{αn},{βn},{γn} are sequences in(0,1).If these sequences satisfy some certain conditions,we can prove that the sequence {xn) which is defined by(3)converges strongly to the fixed point of T.