• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.885-899
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• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.2
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• pp.147-153
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• 2013

Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.345-353
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• 2021

In this paper, first, we present new fixed point theorems for Mönch type multimaps on abstract convex uniform spaces and, also, a fixed point theorem for Mönch type multimaps in Hausdorff KKM L𝚪-spaces. Second, we show that Mönch type multimaps in the better admissible class defined on an L𝚪-space have fixed point properties whenever their ranges are Klee approximable. Finally, we obtain fixed point theorems on 𝔎ℭ-maps whose ranges are 𝚽-sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.30-33
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• 2007

Park and Kim [4], Grabiec [1] studied a fixed point theorem in fuzzy metric space, and Vasuki [8] proved a common fixed point theorem in a fuzzy metric space. Park, Park and Kwun [6] defined the intuitionistic fuzzy metric space in which it is a little revised in Park's definition. Using this definition, Park, Kwun and Park [5] and Park, Park and Kwun [7] proved a fixed point theorem in intuitionistic fuzzy metric space. In this paper, we will prove a common fixed point theorem for a sequence of mappings in a intuitionistic fuzzy metric space. Our result offers a generalization of Vasuki's results [8].

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.159-164
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• 2007

Park, Park and Kwun[6] is defined the intuitionistic fuzzy metric space in which it is a little revised from Park[5]. According to this paper, Park, Kwun and Park[11] Park and Kwun[10], Park, Park and Kwun[7] are established some fixed point theorems in the intuitionistic fuzzy metric space. Furthermore, Park, Park and Kwun[6] obtained common fixed point theorem in the intuitionistic fuzzy metric space, and also, Park, Park and Kwun[8] proved common fixed points of maps on intuitionistic fuzzy metric spaces. We prove a fixed point for pair of maps with another method from Park, Park and Kwun[7] in intuitionistic fuzzy metric space defined by Park, Park and Kwun[6]. Our research are an extension of Vijayaraju and Marudai's result[14] and generalization of Park, Park and Kwun[7], Park and Kwun[10].

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.17-31
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• 2005

In this paper we prove common fixed point theorems for three mappings under the condition of weak compatible mappings, without taking any function continuous in fuzzy metric space and then extend this result to fuzzy 2-metric space and fuzzy 3-metric space.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.321-325
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• 2006

The purpose of this paper is to establish the common fixed point theorem in the intuitionistic fuzzy metric space in which it is a little revised in Park [11]. Our research are an extension of Jungck's common fixed point theorem [8] in the intuitionistic fuzzy metric space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.108-112
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• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.