In this paper, we study the convergence theorems of the Modified Ishikawa iterative sequence with mixed errors for the uniformly continuous mappings and solving nonlinear uniformly continuous mappings equation in arbitrary real Banach space.
In this paper, we introduced some fact in 2-Banach space. Also, we define asymptotically non-expansive mappings in the setting of 2-normed spaces analogous to asymptotically non-expansive mappings in usual normed spaces. And then prove the existence of fixed points for this type of mappings in 2-Banach spaces.
Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.
This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim
... Show MoreIn this article, we will present a quasi-contraction mapping approach for D iteration, and we will prove that this iteration with modified SP iteration has the same convergence rate. At the other hand, we prove that the D iteration approach for quasi-contraction maps is faster than certain current leading iteration methods such as, Mann and Ishikawa. We are giving a numerical example, too.
The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.
The aim of this paper, is to study different iteration algorithms types two steps called, modified SP, Ishikawa, Picard-S iteration and M-iteration, which is faster than of others by using like contraction mappings. On the other hand, the M-iteration is better than of modified SP, Ishikawa and Picard-S iterations. Also, we support our analytic proof with a numerical example.
The aim of this paper is to introduce the concepts of asymptotically p-contractive and asymptotically severe accretive mappings. Also, we give an iterative methods (two step-three step) for finite family of asymptotically p-contractive and asymptotically severe accretive mappings to solve types of equations.