On sequences resulting from iteration of modified quadratic and palindromic mappings

On Sequences Resulting from Iteration of Modified Quadratic and Palindromic Mappings

Blanchard and Fabre (1994) have considered description of symbolic systems by sequences obtained by iteration of two mappings $1, and d,, defined by g,(u) = u[u], and L/, J u[u]:, m here the word [u], is obtained from a word u by removing the last ,j symbols. They stated a conjecture thal the iteration of (I, results in an automatic sequence. We prove here that t/, ix. while (1) 1s not, a 2.aut...

Modified Halpern Iteration of Asymptotically Non-Expansive Mappings

Convergence and Stability of Modified Random SP-Iteration for A Generalized Asymptotically Quasi-Nonexpansive Mappings

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

modified halpern iteration of asymptotically non-expansive mappings

Strong Convergence of a Modified Halpern’s Iteration for Nonexpansive Mappings

A mapping T : C → C is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. We denote by Fix T {x ∈ C : Tx x} the set of fixed points of T . In the last ten years, many papers have been written on the approximation of fixed point for nonlinear mappings by using some iterative processes see, e.g., 1–18 . An explicit iterative process was initially introduced, in 1967, by Halpern 3 i...