• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.611-622
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• 2001

Some convergence theorems of modified Ishikawa and Mann iteration processes with errors for asymptotically pseudo-contractive and asymptotically nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results in Liu [7] and Schu [10].

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.167-174
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• 2012

In this paper, we introduce an asymptotically $\phi$-hemicontractive mapping with a $\phi$-normalized duality mapping and obtain some strongly convergent result of a kind of multi-step iteration schemes for asymptotically $\phi$-hemicontractive mappings.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1271-1284
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• 2018

In this paper, we establish strong convergence of the modified Ishikawa iterates of an asymptotically non expansive self-mapping of a nonempty closed bounded and convex subset of a uniformly convex Banach space under a variety of new control conditions.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.499-512
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• 2022

In this paper, we construct an iteration scheme involving a hybrid pair of the Suzuki generalized nonexpansive single-valued and multi-valued mappings in a complete CAT(0) space. In process, we remove a restricted condition (called end-point condition) in Akkasriworn and Sokhuma's results [2] in Banach spaces and utilize the same to prove some convergence theorems. The results in this paper, are analogs of the results of Akkasriworn et al. [3] in Banach spaces.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.13-23
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• 2009

Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

• East Asian mathematical journal
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• v.27 no.1
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• pp.35-49
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• 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
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• v.49 no.4
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• pp.667-674
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• 2009

In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.493-506
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• 2007

In this paper weak and strong convergence theorems of modified Noor iterations to fixed points for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces are established. In one theorem where we establish strong convergence we assume an additional property of the operator whereas in another theorem where we establish weak convergence assume an additional property of the space.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.127-139
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• 2016

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao's results [Sokhuma and Kaewkhao, Fixed Point Theory Appl. 2010, Art. ID 618767, 9 pp.].

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.235-252
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• 2014

In this paper, weak and strong convergence theorems of three step iteration process with errors are established for two weakly inward and non-self asymptotically nonexpansive mappings in Banach spaces. The results obtained in this paper extend and improve the several recent results in this area.