• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.293-299
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• 2008

In this paper, we prove strong convergence theorems for a finite family of uniformly L-Lipschitzian mappings by a cyclic iterative algorithm in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.793-806
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• 2016

G-vector-valued sequence space frames and g-Banach frames for Banach spaces are introduced and studied in this paper. Also, the concepts of duality mapping and ${\beta}$-dual of a BK-space are used to define frame mapping and synthesis operator of these frames, respectively. Finally, some results regarding the existence of g-vector-valued sequence space frames and g-Banach frames are obtained. In particular, it is proved that if X is a separable Banach space and Y is a Banach space with a Schauder basis, then there exist a Y-valued sequence space $Y_v$ and a g-Banach frame for X with respect to Y and $Y_v$.

• 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.]

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• East Asian mathematical journal
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• v.27 no.1
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• pp.11-21
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• 2011

In this paper, we try to extend the viscosity approximation technique to find a particular common zero of a finite family of accretive mappings in a Banach space which is strictly convex reflexive and has a weakly sequentially continuous duality mapping. The explicit viscosity approximation scheme is proposed and its strong convergence to a solution of a variational inequality is proved.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• East Asian mathematical journal
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• v.25 no.1
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• pp.97-105
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• 2009

In this paper, we prove a strong convergence theorem for a common fixed point of two relatively nonexpansive mappings in a Banach space by using the modified Ishikawa iteration method. Our results improved and extend the corresponding results announced by many others.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.185-190
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• 2005

For the almost certainly convergent series $S_n$ of independent random variables the limiting behavior of tail series ${T_n}{\equiv}S-S_{n-1}$ is reviewed. More specifically, tail series strong laws of large number and tail series weak laws of large numbers will be introduced, and their relationship will be investigated. Then, the relationship will also be extended to the case of Banach space valued random elements, by investigating the duality between the limiting behavior of the tail series of random variables and that of random elements.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.43-51
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• 2002

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multi-valued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.145-150
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• 2015

Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.