Numerical reckoning fixed points via new faster iteration process

Abstract

In this paper, we propose a new iteration process which is faster than the leading S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61-79], Thakur et al. [App. Math. Comp. 275 (2016), 147-155] and M [Filomat 32, no. 1 (2018), 187-196] iterations for numerical reckoning fixed points. Using new iteration process, some fixed point convergence results for generalized α-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes.

A novel iterative approach for split feasibility problem

“…In this paper, we prove some convergence results involving the iteration process (1.1) for generalized α-Reich-Suzuki nonexpansive mappings which is bigger class of mappings than the class of generalized α-nonexpansive mappings. Thus, our results are the genuine generalization of results of Ullah et al [24] and Temir and Korkut [25]. Further, we construct a numerical example which justify the our findings over the the existing iteration processes.…”

“…In this paper we studied the convergence behaviour of an iteration scheme introduced by Ullah et al and Temir and Korkut [25] in respect of generalized α-Reich-Suzuki nonexpansive mapping. Theorems 1, 2 and 3 of our paper are main convergence theorems which generalized the Theorems 3.3 and 3.4 of Ullah et al [24] and Theorem 2.2 and 2.3 of Temir and Korkut [25].…”

“…Motivated by foregoing studies, Ullah et al [24] and Temir and Korkut [25] introduced a new iteration involving generalized α-nonexpansive mappings. If S is a is a mapping on convex subset K of a Banach space E, then the process as follows:…”

Some Fixed-Point Results for the KF-Iteration Process in Hyperbolic Metric Spaces

“…Very recently, in 2022, Ullah et al [16] and Temir and Korkut [17] introduced a new iteration process involving generalized α-nonexpansive mappings. If S is a self-mapping on a convex subset Y of a Banach space X, then the iteration process is stated as follows:…”

“…where {σ n } ∞ n=1 and {η n } ∞ n=1 are real sequences in [0,1]. This iteration is called the KFiteration process by Ullah et al [16]. Throughout this paper, we will use this name for the iteration process (1).…”