• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.775-780
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• 1998

In this paper it is shown that Dunford-Pettis operators obey the "Pettis-divisor property": if T is a Dunford-Pettis operator from $L_1$($\mu$) to a Banach space X, then there is a non-Pettis representable operator S : $L_1$($\mu$)longrightarrow$L_1$($\mu$) such that To S is Pettis representable.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.445-464
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• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1677-1703
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• 2008

In this paper, we introduce and study various locally convex vector topologies on the space of bounded linear operators between Banach spaces. We also apply these topologies to approximation properties.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.65-69
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• 2001

For any closed subspace X of $\ell_p, \; 1<\kappa<\infty$, K(X) is proximinal in L(X), and if X is a Banach space with an unconditional shrinking basis, then K(X, c$_0$) is proximinal in L(X,$ \ell_\infty$).

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.119-124
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• 2001

In the paper we show that some operators defined on L$^1$($\mu$) and on C(K) into Banach space with the RNP have the lifting property.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.151-161
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• 2008

We prove that a countably condensing operator defined on a closed wedge in a Banach space has a fixed point if it is strictly quasibounded, by using an index theory for such operators. From this, the existence of eigenvalues and surjectivity are deduced.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.295-300
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• 1992

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.665-673
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• 2006

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.13-31
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• 2015

In this paper, we introduce a general iterative algorithm for finding a common element of the common fixed point set of an infinite family of ${\lambda}_i$-strict pseudo-contractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in q-uniformly smooth Banach spaces. Then, we analyze the strong convergence of the iterative sequence generated by the proposed iterative algorithm under mild conditions.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.29-40
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• 2003

Let K be a nonempty closed bounded convex subset of an arbitrary smooth Banach space X and T : KlongrightarrowK be a strictly hemi-contractive operator. Under some conditions we obtain that the Mann iteration method with errors both converges strongly to a unique fixed point of T and is almost T-stable on K. The results presented in this paper generalize the corresponding results in [l]-[7], [20] and others.