• Communications of the Korean Mathematical Society
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• v.24 no.1
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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.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.189-200
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• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.

• Korean Journal of Mathematics
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• v.3 no.2
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• pp.187-195
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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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].

• East Asian mathematical journal
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• v.24 no.1
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• pp.111-123
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• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.9-16
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• 1995

D. Dubois and H. Prade introduced the notions of fuzzy numbers and defined its basic operations [3]. R. Goetschel, W. Voxman, A. Kaufmann, M. Gupta and G. Zhang [4,5,6,9] have done much work about fuzzy numbers. Let $\mathbb{R}$ the set of all real numbers and $F^{*}(\mathbb{R})$ all fuzzy subsets defined on $\mathbb{R}$. G. Zhang [8] defined the fuzzy number $\tilde{a}\;\in\;F^{*}(\mathbb{R})$ as follows : (omitted)

• Proceedings of the Korean Statistical Society Conference
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• 2001.11a
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• pp.137-141
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• 2001

We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.181-198
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• 2013

C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.83-90
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• 2013

Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.

• The Pure and Applied Mathematics
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• v.31 no.1
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• pp.83-102
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• 2024

In this paper, first we establish a unique common fixed point theorem satisfying new contractive condition on partially ordered non-Archimedean fuzzy metric spaces and give an example to support our result. By using the result established in the first section of the manuscript, we formulate a unique common coupled fixed point theorem and also give an example to validate our result. In the end, we study the existence of solution of integral equation to verify our hypothesis. These results generalize, improve and fuzzify several well-known results in the existing literature.