• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.621-640
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• 2014

In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1591-1600
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• 2008

In this paper, we introduce an iterative scheme given by infinite nonexpansive mappings in Banach spaces. We prove strong convergence theorems which are connected with the problem of image recovery. Our results enrich and complement the recent many results.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.587-603
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• 2001

The purpose of this paper is to study the nonlinear ergodic theorems and asymptotic behavior for an almost-orbit of asymptotically nonexpansive type mappings in a uniformly convex Banach space with Opial’s condition.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.375-385
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• 2014

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.

• East Asian mathematical journal
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• v.28 no.1
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• pp.81-92
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• 2012

The purpose of this paper is to establish strong convergence of an implicit iteration process to a common fixed point for a finite family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. Our results improve and extend the corresponding results of Fukhar-ud-din et al. [15] and some others from the current literature.

• East Asian mathematical journal
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• v.26 no.5
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• pp.693-702
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• 2010

We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A'), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• East Asian mathematical journal
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• v.29 no.1
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• pp.23-37
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• 2013

The purpose of this paper is to study an implicit iteration process with errors and establish weak and strong convergence theorems to converge to common fixed points for a finite family of generalized asymptotically quasi-nonexpansive mappings in the framework of uniformly convex Banach spaces. Our results extend, improve and generalize some known results from the existing literature.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.131-137
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• 1996

In this paper, we give a necessary and sufficient condition for the weak convergence of trajectories of non-lipschitzian asymptotically nonexpansive mappings.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.777-798
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• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.