• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.847-860
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• 2006

In this paper, some new convergence theorems of the modified Ishikawa and Mann iterative sequences with errors for asymptotically set-valued pseudocontractive mappings in uniformly smooth Banach spaces are given.

• East Asian mathematical journal
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• v.19 no.1
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• pp.103-111
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• 2003

In this paper, we will discuss some sufficient and necessary conditions for modified Ishikawa iterative sequence with mixed errors to converge to fixed points for asymptotically quasi-nonexpansive mappings in Banach spaces. The results presented in this paper extend, generalize and improve the corresponding results in Liu [4,5] and Ghosh-Debnath [2].

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.71-78
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• 2005

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1027-1033
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• 2001

In this paper we obtain the necessary and sufficient conditions for convergence concerning the Mann iterative sequences with errors for the class of continuous accretive operators in smooth Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.295-305
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• 2010

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically $\Phi$-pseudocontractive mappings in real Banach spaces. Finally, we obtain the convergence theorems of Ishikawa iterative sequence and the modified Ishikawa iterative process with errors.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.119-127
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• 2003

The purpose of this paper is to study the necessary and sufficient conditions for the sequences of Ishikawa iterative sequences with mixed errors of asymptotically quasi-nonexpansive type mappings in Banach spaces to converge to a fixed point in Banach spaces. The results presented in this paper extend and improve the corresponding results of［l-4, 7-9].

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.455-469
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• 2002

The Purpose Of this Paper is to introduce the concept of a class of strictly successively hemicontractive mappings and construct certain stable and almost stable iteration procedures for the iterative approximation of fixed points for asymptotically nonexpansive and strictly successively hemicontractive mappings in Banach spaces.