• Communications of the Korean Mathematical Society
• /
• v.28 no.1
• /
• pp.107-121
• /
• 2013

The purpose of this paper is to investigate the demiclosed principle, the existence theorems and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. The structure of fixed point set of such mappings is also studied. Our results generalize, unify and extend several comparable results in the existing literature.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.1
• /
• pp.1-11
• /
• 2021

In this paper we study the weak and strong convergence to minimizers of convex function of proximal point algorithm SP-iteration of three multivalued nonexpansive mappings in a Hilbert space.

• 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.

• Nonlinear Functional Analysis and Applications
• /
• v.23 no.1
• /
• pp.73-95
• /
• 2018

In this paper, we study the existence of fixed points, demiclosedness principle and the structure of fixed point sets for the class of nearly asymptotically nonexpansive nonself-mappings in CAT(0) spaces, and also we discuss the strong and ∆-convergence theorems for an iterative scheme introduced by Khan. Our results are improvements of the various well-known results of fixed point theory which is established in uniformly convex Banach spaces as well as CAT(0) spaces.

• East Asian mathematical journal
• /
• v.28 no.5
• /
• pp.617-630
• /
• 2012

In this paper, the problem of iterative approximation of common fixed points of asymptotically nonexpansive is investigated in the framework of Banach spaces. Weak convergence theorems are established. A necessary and sufficient condition for strong convergence is also discussed. As an application of main results, a variational inequality is investigated.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.473-482
• /
• 2011

In this paper, mappings which are asymptotically pseudo-contractive in the intermediate sense are considered based on a hybrid projection method. Strong convergence theorems of fixed points are established in the framework of Hilbert spaces.

• East Asian mathematical journal
• /
• v.26 no.1
• /
• pp.81-93
• /
• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.2
• /
• pp.381-403
• /
• 2022

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

• East Asian mathematical journal
• /
• v.27 no.1
• /
• pp.35-49
• /
• 2011

In this paper, we study multi-step iterative algorithm with errors and give the necessary and sufficient condition to converge to com mon fixed points for a finite family of asymptotically quasi-nonexpansive type mappings in Banach spaces. Also we have proved a strong convergence theorem to converge to common fixed points for a finite family said mappings on a nonempty compact convex subset of a uniformly convex Banach spaces. Our results extend and improve the corresponding results of [2, 4, 7, 8, 9, 10, 12, 15, 20].

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.433-441
• /
• 2012

We adapt the concept of shrinking projection method of Takahashi et al. [J. Math. Anal. Appl. 341(2008), 276-286] to the iteration scheme studied by Kim and Lee [Kyungpook Math. J. 48(2008), 685-703] for two relatively weak nonexpansive mappings. By letting one of the two mappings be the identity mapping, we also obtain strong convergence theorems for a single mapping with two types of computational errors. Finally, we improve Kim and Lee's convergence theorem in the sense that the same conclusion still holds without the uniform continuity of mappings as was the case in their result.