On a New Faster Implicit Fixed Point Iterative Scheme in Convex Metric Spaces

Abstract

The purpose of this paper is to consider a new implicit iteration and study its strong convergence, stability, and data dependence. It is proved through numerical examples that newly introduced iteration has better convergence rate than well known implicit Mann iteration as well as implicit Ishikawa iteration and implicit iterations converge faster as compared to corresponding explicit iterations. Applications of implicit iterations to RNN (Recurrent Neural Networks) analysis are also presented.

Bazı sabit nokta yineleme yöntemlerinin yakınsama davranışlarının incelenmesi

“…Temel bilimlerin ve mühendisliğin birçok dalında ortaya çıkan doğrusal ve doğrusal olmayan problemler aşağıdaki gibi verilen bir sabit nokta denklemi ile modellenebilirler: [6], [7], [8], [9], [10], [11] ).…”

“…Son zamanlarda, Chugh ve diğ. [7] konvekslik yapısını kullanarak aşağıdaki formda verilen genel bir kapalı yineleme metodu tanımladılar: verilen bir 0 ∈ için…”

Iteration Process for Fixed Point Problems and Zeros of Maximal Monotone Operators

“…Fixed point theory has been revealed as a very powerful and effective method for solving a large number of problems which emerge from real world applications and can be translated into equivalent fixed point problems. In order to obtain approximate solution of the fixed point problems various iterative methods have been proposed (see, e.g., [1][2][3][4][5][6][7][8][9][10] and the reference therein). One of the important instances of fixed point problems is the problem of solving zero point problem of nonlinear operators.…”

On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators

“…In the recent years, numerous papers have been published on the strong convergence and T-stability of various iterative approximations of fixed points for contractive-type operators. See [1][2][3][4][5][6][7][8][9]. The Picard iterative scheme defined for 0 ∈ = −1 , ≥ 1,…”

“…where { } and { } are sequences in [0, 1]. The implicit Noor iteration was defined by Chugh et al [5] as follows:…”