[PDF] Top 20 Strong Convergence of an Implicit Iteration Algorithm for a Finite Family of Pseudocontractive Mappings

... the implicit iteration process ...the strong convergence of the iterative process ...a finite family of pseudocontractive mappings {T i } N i1 ... See full document

... prove strong convergence of Halpern-Ishikawa algorithm ...a finite family of Lipschitz pseudocontractive ...the mappings or on ... See full document

... In this paper we prove the strong convergence of a new iteration scheme to a common fixed point of a finite family of Lipschitz strongly pseudocontractive mappings in a real Banach spac[r] ... See full document

... prove that this iterative scheme converges weakly or strongly to a common fixed point of a finite family of asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in ... See full document

... It is well known that every continuous and demicompact mapping must satisfy condi- tion (A) (see [21]). Since every completely continuous mapping T : K → K is continuous and demicompact, it satisfies condition (A). ... See full document

... the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of ... See full document

... The class of strictly pseudocontractive mappings has been studied by several authors see, e.g., 1–10. It is shown in 4 that a strictly pseudocontractive map is L-Lipschitzian i.e., Tx − Ty ≤ Lx− y, ... See full document

... proved strong convergence theorem for Lipschitzian pseudocontractive mapping in Hilbert space and Qihou [18] extended this result to more general class of Lipschitz hemicontactive ... See full document

... the implicit iteration process (.) and to prove some strong and weak convergence theorems for a continuous pseudocontractive map- ping and a weak convergence theorem for a ... See full document

... Mann iteration algorithm has only weak convergence; see [] for more ...problems, strong convergence is often much more desirable than weak convergence for it translates the ... See full document

... and strong convergence of implicit iter- ation process with errors to a common fixed point for a finite family of nonexpansive mappings in Banach ... See full document

... In , Yao et al. [] introduced the hybrid Mann algorithm as follows. Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let T : C → C be a L-Lipschitz pseudocontractive mapping ... See full document

... Mann iteration scheme has only weak convergence for nonexpansive mappings even in a Hilbert space see ...prove strong convergence theorems for a finite family of accretive ... See full document

... interval [0, 1]. But Mann’s iteration process has only weak convergence, in general. For example, Reich [4] shows that if E is a uniformly convex Banach space and has a Frehet differentiable norm and if the ... See full document

... nonexpansive mappings have been studied by various authors (see, ...hybrid iteration method for nonexpansive mappings in Hilbert space; and then Osilike et ...the strong monotonicity ... See full document

... nonexpansive mappings was introduced by Goebel and Kirk [] in ...Lipschitz pseudocontractive mappings in a Banach ...and strong convergence problems of the iterative algorithms for ... See full document

... of strong convergence of the multi-step iterative algorithm with errors for a finite family of generalized asymptotically quasi-nonexpansive mappings to converge to common fixed ... See full document

... new implicit iteration process with errors for finite families of strictly asymptot- ically pseudocontractive mappings and nonexpansive mappings is ...some strong ... See full document

... the iteration process is defined. If one assumes that the iteration process is always defined, our result will hold for even the more general class of asymptotically hemicontractive maps ...(i.e., ... See full document

... general implicit iterative process which includes Schu’s explicit iterative processes and Sun’s implicit iterative processes as special cases for a finite family of generalized asymptotically ... See full document