• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1409-1418
• /
• 2010

In this paper, we present a preconditioned iterative method for solving linear systems Ax = b, where A is a Z-matrix. We give some comparison theorems to show that the rate of convergence of the new preconditioned iterative method is faster than the rate of convergence of the previous preconditioned iterative method. Finally, we give one numerical example to show that our results are true.

• Journal of applied mathematics & informatics
• /
• v.28 no.5_6
• /
• pp.1499-1506
• /
• 2010

IIn this paper, we suggest and analyze a modified Mann's algorithm based on the CQ method for pseudo-contractive mappings in Hilbert spaces. Further, we prove a strong convergence theorem according to the proposed algorithm for pseudo-contractive mappings.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.3
• /
• pp.513-521
• /
• 2014

Via extension of the classical double-Newton method, we propose high-order family of two-point methods in this paper. Theoretical and computational properties of the proposed methods are fully investigated along with a main theorem describing methodology and convergence analysis. Typical numerical examples are thoroughly treated to verify the underlying theory.

• The Pure and Applied Mathematics
• /
• v.21 no.3
• /
• pp.195-206
• /
• 2014

In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.731-742
• /
• 2022

In this paper, we present a new mixed type iterative process for approximating the common fixed points of single-valued nonexpansive mapping and multi-valued nonexpansive mapping in a CAT(0) space. We demonstrate strong and weak convergence theorems for the new iterative process in CAT(0) spaces, as well as numerical results to support our theorem.

• East Asian mathematical journal
• /
• v.25 no.1
• /
• pp.97-105
• /
• 2009

In this paper, we prove a strong convergence theorem for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the modified Ishikawa iteration method. Our results improved and extend the corresponding results announced by many others.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.515-530
• /
• 2022

A factor graph and belief propagation can be used for finding stochastic values of link weights in biological networks. However it is not easy to follow the process of use and so we presented the process with a toy network of three nodes in our prior work. We extend this work more generally and present numerical example for a network of 100 nodes.

• Journal of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.137-162
• /
• 2014

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < ${\lambda}$ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter ${\lambda}$. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for ${\lambda}=1$.

• East Asian mathematical journal
• /
• v.28 no.1
• /
• pp.63-71
• /
• 2012

The aim of this article is to study an implicit iteration process with errors for a finite family of non-Lipschitzian asymptotically non expansive mappings in the intermediate sense in Banach spaces. Also we establish some strong convergence theorems and a weak convergence theorem for said scheme to converge to a common fixed point for non Lipschitzian asymptotically nonexpansive mappings in the intermediate sense. The results presented in this paper extend and improve the corresponding results of [1], [3]-[8], [10]-[11], [13]-[14], [16] and many others.

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.759-769
• /
• 2005

We first discuss jump discontinuity in higher dimension, and then prove a local convergence theorem for wavelet approximations in higher dimension. We also redefine the concept of Gibbs phenomenon in higher dimension and show that wavelet expansion exhibits Gibbs phenomenon.