• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.4
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• pp.296-299
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• 2012

In this paper, we give definitions for common limit in the range property of mappings and obtain common fixed point theorem for a pair of weakly compatible functions in intuitionistic fuzzy metric space using the joint common limit in the range property of mappings(shortly, (JCLR) property). Our results improve and generalize results of Chauhan et al[1].

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.127-138
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• 2015

The object of this paper is to emphasize the role of 'common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paedagog. Nyhàzi. (N.S.) 24(2) (2008), 257-266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying $\phi$-contractive condition.

• 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.26 no.3
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• pp.111-131
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• 2019

We introduce (CLRg) property for hybrid pair $F:X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$. We also introduce joint common limit range (JCLR) property for two hybrid pairs $F,G:X{\times}X{\rightarrow}2^X$ and $f,g:X{\rightarrow}X$. We also establish some common coupled fixed point theorems for hybrid pair of mappings under generalized (${\psi},{\theta},{\varphi}$)-contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. As an application, we study the existence and uniqueness of the solution to an integral equation. We also give an example to demonstrate the degree of validity of our hypothesis. The results we obtain generalize, extend and improve several recent results in the existing literature.

• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• The Korean Journal of Air & Space Law and Policy
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• v.33 no.2
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• pp.169-197
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• 2018

The purpose of this study is to present a reasonable and concrete standard for the Korean aviation insurance compulsory subscription system. Through this, we aim to improve the current revision of laws and regulations, and ultimately create an environment in which the safety and property of the Korean people who use aircraft with appropriate aviation insurance can be secured. In particular, by reviewing the aviation business law and its new laws and regulations enacted in 2017, the legislative improvement direction of aviation insurance will be proposed. In order to maintain the continuous growth of the air transportation industry and to make amicable compensation for the victims, considering the characteristics of the total accident, instantness, and giganticness of air accidents in which a lot of people and property are lost in the event of an accident, adequate insurance coverage is essential. In this respect, the compulsory insurance to amend the principle of freedom of contract, which is the great principle of the modern judicial system, will be persuasive. However, in comparison with foreign legislation, the legal provisions on Korea's obligation to comply with aviation insurance need to be revised around the following issues: First, it is reasonable to enforce the regulation of the mandatory aviation insurance by legislation from the Congress not by administrative regulations. Because it will force the monetary obligations of the individual such as common air carriers. Second, our law regulations respond to various kinds of air damages by using the phrase "limit of liability stipulated in international conventions". However, as we have seen in the text, the range of compensation are various according to the use of legal instruments in international conventions such as the Montreal Convention, which governs the compensation of passengers for damages to passengers today. Third, in countries with narrow territories, such as Korea, there are big differences in flying time and insurable risk between domestic and international transportation. Therefore, it is necessary to divide domestic transportation and international transportation even in the obligation to join the insurance. This dual discipline has the advantage for rookies in air carrier market who mainly start their business from domestic service. Fourth, according to Korean law, the regulations of automobile loss insurance is applicable to the aviation mandatory insurance of unmanned aerial vehicle accident which is lack of persuasion. In the future, it will be appropriate to discipline insurance for unmanned aerial vehicles with unlimited potential for development from a long-term perspective.