• 대한수학회논문집
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• 제13권3호
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• pp.501-513
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• 1998

In this paper, we deal with the asymptotic behavior for the almost-orbits {u(t)} of an asymptotically nonexpansive semigroup S = {S(t) : t $\in$ G} for a right reversible semitopological semigroup G, defined on a suitable subset C of Banach spaces with the Opial's condition, locally uniform Opial condition, or uniform Opial condition.

• 대한수학회논문집
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• 제12권2호
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• pp.237-250
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• 1997

In this paper, we study the asymptotic behavior of orbits ${S(t)x}$ of an asymptotically nonexpansive semigroup $S = {S(t) : t \in G}$ for a right reversible semitopological semigroup G, defined on a weakly compact convex subset C of Banach spaces with Opial's condition for any $x \in C$.

• Korean Journal of Mathematics
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• 제10권1호
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• pp.19-23
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• 2002

Let X be a Banach space satisfying Opial's condition, C a weakly compact convex subset of $X,F:C{\rightarrow}X$ a nonexpansive map, and let $G:C{\rightarrow}X$ be a compact and demiclosed map. We prove that F + G has a fixed point in C if $F+G:C{\rightarrow}X$ is a weakly inward map.

• 대한수학회보
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• 제38권3호
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• pp.587-603
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• 2001

The purpose of this paper is to study the nonlinear ergodic theorems and asymptotic behavior for an almost-orbit of asymptotically nonexpansive type mappings in a uniformly convex Banach space with Opial’s condition.

• 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.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.71-82
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• 2012

In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.325-336
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• 2008

In this paper, we prove the weak and strong convergence of the three-step iterative scheme with errors to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.525-536
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• 2007

In this paper, we prove the weak and strong convergence of the Noor iterative scheme to a common fixed point for two asymptotically nonexpansive mappings in a uniformly convex Banach space under a condition weaker than compactness. Our theorems improve and generalize some previous results.

• 충청수학회지
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• 제3권1호
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• pp.103-110
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• 1990

Let K be a nonempty weakly compact convex subset of a Banach space X and T : K ${\rightarrow}$ C(X) a nonexpansive mapping satisfying $P_T(x){\cap}clI_K(x){\neq}{\emptyset}$. We first show that if I - T is semiconvex type then T has a fixed point. Also we obtain the same result without the condition that I - T is semiconvex type in a Banach space satisfying Opial's condition. Lastly we extend the result of [5] to the case, that T is an 1-set contraction mapping.

• 대한수학회보
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• 제49권4호
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].