• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1275-1284
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• 2001

In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.617-631
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• 2012

In this paper, we will consider some existence theorems of common fixed points for a countable family of non-self multi-valued mappings defined on a closed subset of a complete metrically convex space, and give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results in this paper generalize and improve many common fixed point theorems for single valued or multi-valued mappings with contractive type conditions.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.45-58
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• 2022

In this paper, iterative algorithms for approximating a common fixed point of a countable family of multi-valued demicontractive maps in the setting of Hadamard spaces are presented. Under different mild conditions, the sequences generated are shown to strongly convergent and ∆-convergent to a common fixed point of the considered family, accordingly. Our theorems complement many results in the literature.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.335-351
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• 2013

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.29-36
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• 1998

We show that if M is a $II_1$-factor and a countable discrete group G acts outerly on M then Jones' index $[M:M^G]$ of a pair of $II_1^-factors is equal to the order $\mid$G$\mid$ of G. It is also shown that for a subgroup H of G Jones' index $[M^H:M^G]$ is equal to the group index [G:H] under certain conditions.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.425-433
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• 2009

In this paper, we give the internal characterizations of compact-covering s-(resp., ${\pi}$-)images of locally separable metric spaces. As applications of these results, we obtain characterizations of compact-covering quotient s-(resp., ${\pi}$-)images of locally separable metric spaces.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1591-1600
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• 2008

In this paper, we introduce an iterative scheme given by infinite nonexpansive mappings in Banach spaces. We prove strong convergence theorems which are connected with the problem of image recovery. Our results enrich and complement the recent many results.

• Kyungpook Mathematical Journal
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• v.28 no.1
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• pp.79-82
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• 1988

This paper investigates the relationship between compactness and pseudo-compactness in subsets of C(X) where X is locally compact and first countable. Two primary theorems are proven. First, equicontinuity at a point is proven to be equivalent to the existence of a certain open cover of a pseudo-compact subset of C(X). The second theorem proves the equivalence of compactness and pseudo-compctness for closed subsets F of C(X).

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.523-558
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• 2021

In this paper, we study some fixed point properties of n-generalized Bregman nonspreading mappings in reflexive Banach space. We introduce a hybrid iterative scheme for finding a common solution for a countable family of equilibrium problems and fixed point problems in reflexive Banach space. Further, we give some applications and numerical example to show the importance and demonstrate the performance of our algorithm. The results in this paper extend and generalize many related results in the literature.