• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.81-89
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• 2007

In this paper, we introduce the concept of a system of asymptotically quasinonexpansive type mappings. Furthermore, we define a $k$-step iterative sequence approximating common fixed point for a system of asymptotically quasi-nonexpansive type mappings and study its stability in real Banach spaces.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.279-296
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• 2012

In this paper, we define a generalized duality mapping, which is a generalization of the normalized duality mapping and using this, we extend the notion of a generalized projection and study their properties. Also we construct an approximating fixed point sequence using the generalized projection with the generalized duality mapping and prove its strong convergence.

• 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.

• East Asian mathematical journal
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• v.24 no.2
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• pp.191-199
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• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.661-670
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• 2005

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.1007-1020
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• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.

• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.