• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.621-633
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• 2014

In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

• 충청수학회지
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• 제23권4호
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• pp.801-812
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• 2010

In this paper, we consider the convergence of the shrinking projection method for quasi-$\phi$-nonexpansive mappings. Strong convergence theorems are established in a uniformly smooth and strictly convex Banach space which enjoys the Kadec-Klee property.

• 대한수학회논문집
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• 제27권1호
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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.

• 대한수학회보
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• 제46권5호
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• pp.885-894
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• 2009

In this paper, we consider a hybrid projection algorithm for a pair of inverse-strongly monotone mappings and a quasi-$\phi4-nonexpansive mapping. Strong convergence theorems are established in the framework of Banach spaces.

• 충청수학회지
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• 제23권1호
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• pp.73-82
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• 2010

In an infinite-dimensional Hilbert space, the normal Mann iteration has only weak convergence, in general, even for nonexpansive mappings. The purpose of this paper is to modify the normal Mann iteration to have strong convergence for a closed quasi-$\phi$-nonexpansive mapping in the framework of Banach spaces.

• East Asian mathematical journal
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• 제25권2호
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.