• 대한수학회보
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• 제38권3호
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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].

• Korean Journal of Mathematics
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• 제20권3호
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• pp.353-360
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• 2012

In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.565-580
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• 2021

In this paper, first of all we prove a fixed point theorem for 𝜓_∫𝜑-weakly contractive mapping. Next, we prove some common fixed point theorems for a pair of weakly compatible self maps along with E.A. property and (CLR) property. An example is also given to support our results.

• 대한수학회논문집
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• 제17권1호
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• pp.37-51
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• 2002

Let X be a reflexive Banach space with a uniformly Gateaux differentiable norm, C a nonempty bounded open subset of X, and T a continuous mapping from the closure of C into X which is locally pseudo-contractive mapping on C. We show that if the closed unit ball of X has the fixed point property for nonexpansive self-mappings and T satisfies the following condition: there exists z $\in$ C such that ∥z-T(z)∥<∥x-T(x)∥ for all x on the boundary of C, then the trajectory tlongrightarrowz$_{t}$$\in$C, t$\in$[0, 1) defined by the equation z$_{t}$ = tT(z$_{t}$)+(1-t)z is continuous and strongly converges to a fixed point of T as t longrightarrow 1￣.ow 1￣.

• 대한수학회논문집
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• 제26권3호
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• pp.473-482
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• 2011

In this paper, mappings which are asymptotically pseudo-contractive in the intermediate sense are considered based on a hybrid projection method. Strong convergence theorems of fixed points are established in the framework of Hilbert spaces.

• Korean Journal of Mathematics
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• 제31권3호
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• pp.269-294
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• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.

• Korean Journal of Mathematics
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• 제11권2호
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• pp.111-115
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• 2003

Under some asymptotical conditions we obtain a fixed point theorem for a mapping(not necessarily nonexpansive) from an unbounded closed convex subset of a reflexive Banach space into itself. Also we give an example for applying it.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1499-1506
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• 2010

IIn this paper, we suggest and analyze a modified Mann's algorithm based on the CQ method for pseudo-contractive mappings in Hilbert spaces. Further, we prove a strong convergence theorem according to the proposed algorithm for pseudo-contractive mappings.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1053-1071
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• 2022

The purpose of this article is to establish some fixed point theorems, a common fixed point theorem and a coincidence point theorem via contractive type condition in the framework of complete partial metric spaces and give some examples in support of our results. As an application to the results, we give some fixed point theorems for integral type contractive conditions. The results presented in this paper extend and generalize several results from the existing literature.

• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.