• Communications of the Korean Mathematical Society
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• v.10 no.1
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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].

• Nonlinear Functional Analysis and Applications
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• v.29 no.2
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• pp.477-485
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• 2024

In this work, we will generalize the notion of multivalued (ν, 𝒞)-contraction mapping in 𝑏-Menger spaces and we shall give a new fixed point result of this type of mappings. As a consequence of our main result, we obtained the corresponding fixed point theorem in fuzzy 𝑏-metric spaces. Also, an example will be given to illustrate the main theorem in ordinary 𝑏-metric spaces.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.201-217
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• 2011

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.733-743
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• 2012

In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15].

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.3
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• pp.228-231
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• 2000

More generalized common fixed point theorems for a sequence of fuzzy mappings to the nonexpansive case on Menger probabilistic metric spaces, which generalize recent results of Lee et al.[13], are obtained.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.11-23
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• 2013

In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

• East Asian mathematical journal
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• v.23 no.1
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• pp.123-133
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• 2007

In this paper we prove common fixed point theorem for four mappings, under the condition of compatible mappings of type ($\alpha$) in Menger space, without taking any function continuous. We improve results of Pathak, Kang and Baek [13] and Cho, Murthy and Stojakovic [37].

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.789-807
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• 2015

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.133-144
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• 2003

The aim of this paper is to prove some common fixed point theorems for the class of compatible maps to larger class of weakly compatible maps without appeal to continuity in Monger spaces and we also give a set of alternative conditions in place of completeness of the space. We improve and extend the results of Dedeic & Sarapa ［A common fixed point theorem for three mappings on Monger spaces. Math. Japon. 34 (1989), no. 6,919-923］ and Rashwan & Hedar ［On common fixed point theorems of compatible mappings in Monger spaces. Demonstratio Math. 31 (1998), no. 3, 537-546］.

• Journal of the Korean Mathematical Society
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• v.19 no.2
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• pp.135-141
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• 1983