• The Pure and Applied Mathematics
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• v.28 no.3
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• pp.253-266
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• 2021

In this paper, we generalize the notion of comparable set-valued mappings by introducing two types of 𝓡-closed set-valued mappings and utilize these to obtain an analogue of celebrated Mizoguchi and Takahashi fixed point theorem in relational metric spaces. To annotate the claims and usefulness of such findings, we prove fixed point results for both set-valued and single-valued mappings and validate the assertions with the help of examples. In this way, these investigations extend, modify and generalize some prominent recent fixed point results obtained by Tiammee and Suantai [24], Amini-Harandi and Emami [4], Prasad and Dimri [19] and several others in the settings of relational metric spaces.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1245-1260
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• 2001

A demi-closed theorem and some new weak convergence theorems of iterative sequences for asymptotically nonexpansive and nonexpansive mappings in Banach spaces are obtained. The results presented in this paper improve and extend the corresponding results of [1],[8]-[10],[12],[13],[15],[16], and [18].

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.184-189
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• 2001

First, we find the characterization of fg-closure of a fuzzy set. Second, we study some properties of frg-closeds and fg-continuous mappings. Finaly, we introduce the concept of a fuzzy approximately continuous mapping and study its properties.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.4
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• pp.617-631
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• 2012

In this paper, we will consider some existence theorems of common fixed points for a countable family of non-self multi-valued mappings defined on a closed subset of a complete metrically convex space, and give more generalized common fixed point theorems for a countable family of single-valued mappings. The main results in this paper generalize and improve many common fixed point theorems for single valued or multi-valued mappings with contractive type conditions.

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.261-278
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized closed and open sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy alpha generalized continuous mappings and then investigate some of their properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.2
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• pp.119-123
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• 2010

We introduce and investigate the concepts of ($T_i,T_j$)-fuzzy $\beta$-(r, s)-open sets, ($T_i,T_j$)-fuzzy $\beta$-(r, s)-closed sets and fuzzy pairwise $\beta$-(r, s)-continuous mappings in smooth bitopological spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.129-130
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• 2008

In this paper, we introduce the concept of generalized fuzzy (r,s)-closed sets on intuitionistic fuzzy topological spaces in ${\v{S}ostak's$ sense. Using this concept, we introduce the notions of generalized fuzzy (r,s)-continuous mappings, and then we investigate some of their properties.

• East Asian mathematical journal
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• v.16 no.1
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• pp.125-133
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• 2000

Weak forms of regular continuity and regular closure are introduced and used to strengthen some results concerning the preservation of rg-closed sets.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.189-195
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• 2013

PosM is a category whose objects are ample spaces and morphisms are possibility mappings. We study some properties of the Category PosM. So we show that Category PosM is a cartesian closed category, and it forms a topos with some condition.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.39-46
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• 2017

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.