• 대한수학회지
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• 제53권5호
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• pp.1037-1056
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• 2016

In this paper, we define the concepts of commute proximally, dominate proximally, weakly dominate proximally, proximal generalized ${\varphi}$-contraction and common best proximity point in probabilistic Menger space. We prove some common best proximity point and common fixed point theorems for dominate proximally and weakly dominate proximally mappings in probabilistic Menger space under certain conditions. Finally we show that proximal generalized ${\varphi}$-contractions have best proximity point in probabilistic Menger space. Our results generalize many known results in metric space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권4호
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• pp.245-254
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• 2003

In this paper we prove common fixed point theorems for four mappings, under the condition of weakly compatible mappings in Menger spaces, without taking any function continuous. We improve results of [A common fixed point theorem for three mappings on Menger spaces. Math. Japan. 34 (1989), no. 6, 919-923], [On common fixed point theorems of compatible mappings in Menger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546].

• Korean Journal of Mathematics
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• 제31권4호
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• pp.391-403
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• 2023

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C^*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.523-533
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• 2006

In this paper we have a common fixed point theorem which is a generalization of result of [12] and we characterize the conditions for continuous self mappings S, T of complete fuzzy metric space (X, M, *) have a uniqe common fixed point in X.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.629-643
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• 2019

In common fixed point problems in metric spaces several versions of weak commutativity have been considered. Mappings which are not compatible have also been discussed in common fixed point problems. Here we consider common fixed point problems of non-compatible and R-weakly commuting mappings in probabilistic semimetric spaces with the help of a control function. This work is in line with research in probabilistic fixed point theory using control functions. Further we support our results by examples.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.807-817
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• 2016

The aim of this paper is to introduce the notion of ${\epsilon}$-compatible maps and obtain some common fixed point theorems. Also, our results generalize some well known fixed point theorems.

• 대한수학회보
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• 제45권3호
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• pp.573-585
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• 2008

A few sufficient conditions for the existence and uniqueness of fixed point and common fixed point for certain contractive type mappings in complete metric spaces are provided. Several existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in dynamic programming are discussed by using the fixed point and common fixed point theorems presented in this paper.

• East Asian mathematical journal
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• 제27권5호
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• pp.573-583
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• 2011

In this paper, we prove a common fixed point theorem for noncompatible, discontinuous mappings on a Banach space. Our main theorem extends, improves, generalizes some known results on Banach spaces.

• 호남수학학술지
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• 제38권2호
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• pp.213-229
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• 2016

In this paper, we utilize an implicit relation to improve and extend some strict common fixed point results of the existing literature to two pairs of hybrid mappings in 2-metric spaces via altering distances. As an application, we also prove some strict common fixed point theorems for hybrid pairs of mappings satisfying a contractive condition of integral type in 2-metric spaces.

• 한국지능시스템학회논문지
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• 제16권3호
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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.