• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.961-969
• /
• 2021

In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.

• Honam Mathematical Journal
• /
• v.39 no.1
• /
• pp.1-25
• /
• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.973-985
• /
• 2010

We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.

• Kyungpook Mathematical Journal
• /
• v.59 no.4
• /
• pp.665-678
• /
• 2019

We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].

• Korean Journal of Mathematics
• /
• v.32 no.1
• /
• pp.59-72
• /
• 2024

In the presented paper, the first section contains strong convergence and demiclosedness property of a sequence generated by Karakaya et al. iteration scheme in a Hilbert space for quasi-nonexpansive mappings and also the comparison between the iteration scheme given by Karakaya et al. with well-known iteration schemes for the convergence rate. The second section contains some applications of the fixed point theory in solution of different mathematical problems.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.4
• /
• pp.785-795
• /
• 2022

In this paper, we introduce a Mann-like three step iteration method and show that it can be used to approximate the fixed point of a weak contraction mapping. Furthermore, we prove that this scheme is equivalent to the Mann iterative scheme. A comparison is made with the other third order iterative methods. Results are presented in a table to support our conclusion.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.1
• /
• pp.59-82
• /
• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• Communications of the Korean Mathematical Society
• /
• v.30 no.3
• /
• pp.209-219
• /
• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• Communications of the Korean Mathematical Society
• /
• v.31 no.4
• /
• pp.713-727
• /
• 2016

In this paper, we introduce two general iteration schemes with bounded error terms and prove some theorems related to the strong and ${\Delta}$-convergence of these iteration schemes for multi-valued maps in a hyperbolic space. The results which are presented here extend and improve some well-known results in the current literature.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.41 no.3
• /
• pp.17-24
• /
• 2004

We present a P-type iterative learning control(ILC) scheme for uncertain robotic systems that perform the same tasks repetitively. The proposed ILC scheme comprises a linear feedback controller consisting of position error, and a feedforward and feedback teaming controller updated by current velocity error. As the learning iteration proceeds, the joint position and velocity mrs converge uniformly to zero. By adopting the learning gain dependent on the iteration number, we present joint position and velocity error bounds which converge at the arbitrarily tuned rate, and the joint position and velocity errors converge to zero in the iteration domain within the adopted error bounds. In contrast to other existing P-type ILC schemes, the proposed ILC scheme enables analysis and tuning of the convergence rate in the iteration domain by designing properly the learning gain.