• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.277-286
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• 2003

In this paper, the Monger Probabilistic n-metric space is presented, some Hex point theorem for set valued mapping are extended to Monger probabilistic n-metric space.

• 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.

• 대한수학회논문집
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• 제24권1호
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• pp.17-27
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• 2009

In the present work, we introduce two types of compatible maps and prove a common fixed point theorem for such maps in Menger probabilistic metric spaces. Our result generalizes and extends many known results in metric spaces and fuzzy metric spaces.

• 호남수학학술지
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• 제9권1호
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• pp.77-81
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• 1987

In this paper we introduce the notion of expansion mapping on a probabilistic metric space and prove common fixed point theorems for a pair of such mappings. These results being new of their kind. are interesting generafizations of some of the known results.

• 호남수학학술지
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• 제6권1호
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• 대한수학회논문집
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• 제10권1호
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• pp.67-83
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• 1995

The notion of probabilistic metric spaces (or statistical metric spaces) was introduced and studied by Menger [19] which is a generalization of metric space, and the study of these spaces was expanede rapidly with the pioneering works of Schweizer-Sklar [25]-[26]. The theory of probabilistic metric spaces is of fundamental importance in probabilistic function analysis. For the detailed discussions of these spaces and their applications, we refer to [9], [10], [28], [30]-[32], [36] and [39].

• 대한수학회논문집
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• 제10권1호
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• pp.57-65
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• 1995

Let R denote the set of real numbers, $R_+$ the non-negative real numbers and D and set of all distribution functions.(omitted)

• 대한수학회논문집
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• 제11권1호
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• pp.89-108
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• 1996

In this paper we obtain common fixed point theorems for sequences of fuzzy mappings on Menger probabilistic metric spaces, including common fixed point theorems for sequences of multi-valued mappings, which generalize and improve some results of Lee et al. [8] and Chang [2].

• 대한수학회보
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• 제33권4호
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• pp.565-585
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• 1996

In 1976, Caristi [1] established a celebrated fixed point theorem in complete metric spaces, which is a very useful tool in the theory of nonlinear analysis. Since then, several generalizations of the theorem were given by a number of authors: for instances, generalizations for single-valued mappings were given by Downing and Kirk [4], Park [11] and Siegel [13], and the multi-valued versions of the theorem were obtained by Chang and Luo [3], and Mizoguchi and Takahashi [10].

• 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.