On the Stability and Strong Convergence for Jungck-Agarwal et al. Iteration Procedure

Abstract

In this paper we introduce the Jungck-Agarwal et al. iteration procedure and obtain strong convergence as well as stability results for a pair of non-self mappings. The results obtained are generalization of some existing results in the literature. In addition, we show that the rate of convergence of this newly defined iteration procedure is better than Jungck-Mann, Jungck-Ishikawa and Jungck-Noor iteration procedures. General TermsComputational Mathematics.

Analyzing Stability and Data Dependence Notions by a Novel Jungck-Type Iteration Method

“…Many researchers have worked on this method introduced by Jungck and have obtained many fixed point theorems by rewriting the classical iteration methods in Jungck type. Some of the works done with this approach are as follows for [23] is defined as under:…”

“…Jungck-CR iteration is defined by [24]: 3, the following Jungck-type Agarwal iteration method is obtained [25]: 3, the following Jungck-type Sahu iteration method is obtained [25]:…”

Stability and Data Dependence Results for Jungck-type Iteration Scheme

“…This scheme is very useful to approximate the common and coincidence points of the mappings. For more details on non-self mappings, the reader is referred to [9][10][11][12][13][14][15][16][17][18][19][20].…”

“…where [14] defined a special case of the Jungck-Khan (J-Khan Special) iteration scheme [17] as 1 ( 1) ,…”

An empirical study of the convergence area and convergence speed of Agarwal et al. fixed point iteration procedure

“…Many iterative processes for the approximation of fixed points have been described in the literature [3][4][5][6]. In the following, assume that each iteration process starts from any initial point x 0 ∈ X.…”