• East Asian mathematical journal
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• v.31 no.3
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• pp.301-310
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• 2015

In this paper, we establish a strong convergence for the Noor iterative scheme associated with Lipschitz strongly pseudocontractive mappings in real Banach spaces. It's proof-method is very simple by comparing with the previous proofs known.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.635-644
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• 2008

In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• 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.