• East Asian mathematical journal
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• 제18권2호
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• pp.261-270
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• 2002

We obtain the convergence of three-step iteration methods and generalized three-step iteration methods for quasi-contractive and generalized quasi-contractive mappings, respectively, in Banach spaces. Our results extend the corresponding results in [1], [4]-[6].

• 대한수학회지
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• 제34권3호
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• pp.501-503
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• 1997

The existence of a unique local generalized solution for the abstract functional evolution problem of the type $$ (FDE:\phi) x'(t) + A(t, x_t)x(t) \ni G(t, x_t), t \in [0, T], x_0 = \phi $$ in a general Banach spaces is considered. It is shown that $(FDE:\phi)$ could be considered with well-known fixed point theory and recent results for the functional differential equations involving the operator A(t).

• 대한수학회지
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• 제48권3호
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• pp.585-597
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• 2011

We prove the existence and uniqueness of classical solutions for a quasilinear delay integrodifferential equation in Banach spaces. The result is established by using the semigroup theory and the Banach fixed point theorem.

• 대한수학회지
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• 제57권3호
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• pp.617-640
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• 2020

In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.

• 대한수학회보
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• 제43권4호
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• pp.771-790
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• 2006

The iterative algorithms with errors for nonexpansive mappings are investigated in Banach spaces. Strong convergence theorems for these algorithms are obtained. Our results improve the corresponding results in [5, 13-15, 23, 27-29, 32] as well as those in [1, 16, 19, 26] in framework of a Hilbert space.

• 대한수학회보
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• 제43권4호
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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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• 제26권1호
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• pp.81-93
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• 2010

In this paper, a strong convergence theorem of multi-step iterative schemes with errors for asymptotically quasi-nonexpansive type nonself mappings is established in a real uniformly convex Banach space. Our results extend the corresponding results of Wangkeeree [12], Xu and Noor [13], Kim et al.[1,6,7] and many others.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.201-209
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• 2006

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : $C{\rightarrow}C$ be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

• 대한수학회논문집
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• 제11권1호
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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.

• 대한수학회논문집
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• 제13권4호
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• pp.765-773
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• 1998

Let E be a smooth Banach space. Suppose T : E longrightarrow E is a strongly accretive map. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods), under suitable conditions, converges strongly to a solution of the equation Tx = f.