Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings

Abstract

In this paper, we introduce a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings. Furthermore, we prove that the proposed iterative algorithm converges strongly to a fixed point of a non-expansive mapping in Hilbert spaces.

Strong Convergence of a Modified Ishikawa Iterative Algorithm for Lipschitz Pseudocontractive Mappings

“…It is our purpose in this paper to complement Yao, Xu and Liou [12]; and Maingé and Mǎruşter [14] by introducing a modified Ishikawa iteration algorithm analogous to the modified Mann iteration algorithm studied in [12] and [14]. We further prove that our modified Ishikawa algorithm converges strongly to a fixed point of a Lipschitz pseodocontive map in real Hilbert spaces.…”

“…Observe that as in the case of the modified Mann iteration algorithm of [12] and [14], our modified Ishikawa iteration scheme reduces to the normal Ishikawa iteration when t n ≡ 0.…”

“…Recently Yao, Zhou and Liou [12] (see also [13]) studied a modified Mann iteration algorithm and proved strong convergence of the modified algorithm to a fixed point of a nonexpansive mapping in real Hilbert spaces. They proved the following.…”

A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces

“…where T is a nonexpansive mapping. The solution set of this equation coincide to a fixed points set of T. Such operators have been studied extensively (see, e.g., Yao et al [24], Chidume [4], Marino et al [15] and the references therein).…”

A new iterative algorithm for solving some nonlinear problems in Hilbert spaces

“…The crucial key of this success is due to the possibility of representing various problems arising in the above disciplines, in the form of an equivalent fixed point problem. Until now there have been many effective algorithms for solving fixed point problem (see, e.g., Yao et al [35], Chidume [4], Marino et al [16], Xu [30,31], and the references therein).…”