• East Asian mathematical journal
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• v.36 no.5
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• pp.593-604
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• 2020

Let the circle act on a compact oriented manifold with a discrete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S¹ near the fixed point. In this paper, we provide the author's original proof that only uses the Atiyah-Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite number of fixed points.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.522-525
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• 1998

Although each de Morgan algebra has not always fixed points(centers), it has always fixed cores, the natural extention of fixed points. Fixed cores, of they do not degenerate to fixed points, are Boolean algebras, It is also shown the necessary and sufficient condition a algebra to be a Kleene algebra(fuzzy algebra) is that it has just one fixed core.

• East Asian mathematical journal
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• v.37 no.1
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• pp.123-130
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• 2021

In this paper, we introduce the new concept of a cone metric-like space and consider some fixed point theorems for generalized contractive mappings under suitable conditions in cone metric-like spaces. Our results generalize and unify the several main results of [1, 2, 9].

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.575-585
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• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• East Asian mathematical journal
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• v.18 no.1
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• Honam Mathematical Journal
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• v.35 no.3
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• pp.389-394
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• 2013

It is an interesting problem to study fixed points of an element in the holonomy group of an affine manifold. We compute the limit of a sequence of projective transformations and verify relations between fixed points and kernels.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.275-284
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• 2011

In this note we study the Schwarz lemma and its various versions. We find a condition for a holomorphic map to have fixed points only on the boundary of the unit disc and compare its derivatives at fixed points to get some relations among them.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.91-97
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• 2000

In this paper we obtain a criterion for the existence of a common fixed point of a pair of mappings in 2-metric spaces. Our result generalizes a number of fixed point theorems given by Imdad, Khan and Khan [1], Kahn and Fisher [2], Kubiak [3], Rhoades [5], and Singh, Tiwari and Gupta [6].

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1725-1740
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• 2008

In this paper, we introduce a fixed point index of weakly inward 1-set-contraction mappings. With the aid of the new index, we obtain some new fixed point theorems, nonzero fixed point theorems and multiple positive fixed points for this class of mappings. As an application of nonzero fixed point theorems, we discuss an eigenvalue problem.