Double newtonisation of fixed point sequences
نویسنده
چکیده
A neutral fixed point of a real iteration map u becomes a super attracting fixed point using a suitable double newtonisation. The map u is so transformed into a map w which is here called the standard accelerator of u. The map w provides a unifying process to deal with a large set of fixed point sequences which are not convergent or converge slowly. Several examples illustrate the main results obtained. MSC2000: 65B, 65H05, 65B99.
منابع مشابه
Iterative scheme based on boundary point method for common fixed point of strongly nonexpansive sequences
Let $C$ be a nonempty closed convex subset of a real Hilbert space $H$. Let ${S_n}$ and ${T_n}$ be sequences of nonexpansive self-mappings of $C$, where one of them is a strongly nonexpansive sequence. K. Aoyama and Y. Kimura introduced the iteration process $x_{n+1}=beta_nx_n+(1-beta_n)S_n(alpha_nu+(1-alpha_n)T_nx_n)$ for finding the common fixed point of ${S_n}$ and ${T_n}$, where $uin C$ is ...
متن کاملDouble Sequence Iterations for Strongly Contractive Mapping in Modular Space
In this paper, we consider double sequence iteration processes for strongly $rho$-contractive mapping in modular space. It is proved, these sequences, convergence strongly to a fixed point of the strongly $rho$-contractive mapping.
متن کاملFixed Point Results on $b$-Metric Space via Picard Sequences and $b$-Simulation Functions
In a recent paper, Khojasteh emph{et al.} [F. Khojasteh, S. Shukla, S. Radenovi'c, A new approach to the study of fixed point theorems via simulation functions, Filomat, 29 (2015), 1189-–1194] presented a new class of simulation functions, say $mathcal{Z}$-contractions, with unifying power over known contractive conditions in the literature. Following this line of research, we extend and ...
متن کاملAIOSC: Analytical Integer Word-length Optimization based on System Characteristics for Recursive Fixed-point LTI Systems
The integer word-length optimization known as range analysis (RA) of the fixed-point designs is a challenging problem in high level synthesis and optimization of linear-time-invariant (LTI) systems. The analysis has significant effects on the resource usage, accuracy and efficiency of the final implementation, as well as the optimization time. Conventional methods in recursive LTI systems suffe...
متن کاملA Shorter and Simple Approach to Study Fixed Point Results via b-Simulation Functions
The purpose of this short note is to consider much shorter and nicer proofs about fixed point results on b-metric spaces via b-simulation function introduced very recently by Demma et al. [M. Demma, R. Saadati, P. Vetro, emph{Fixed point results on b-metric space via Picard sequences and b-simulation functions}, Iranian J. Math. Sci. Infor. 11 (1) (2016) 123--136].
متن کامل