Study Of Convergence Of Two Iterations For Semigroup In Banach Space

A hybrid iteration algorithm relative to a class of quasi-?-asymptotically nonexpansive semigroups and modify the normal Mann's iterative algorithm was introduced to have the strong convergence, a sequence produced by this hybrid iteration is located in a closed and convex set by using the generalized projection in Banach space and then this sequence converges to a common fixed point of quasi-?-asymptotically nonexpansive semigroups is proved in a strictly convex, reflexive, smooth Banach spaces with K-K property and Lyapunov functional. The convergence study and introduce a class of iterative for asymptotically nonexpansive semigroups by using some properties in a uniformly convex Banach space.Four chapters included in this thesis:Chapter One introduces the origin of the two iterations and main research content.Chapter Two provides some prerequisite of this thesis.Chapter Three analyze strong convergence theorems for quasi-?-asymptotically nonexpansive semigroups of the hybrid iteration algorithm.Chapter Four analyze strong convergence theorems for asymptotically nonexpansive semigroups.