• 호남수학학술지
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• 제43권2호
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• pp.305-323
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• 2021

In the present paper, utilizing (𝜙, 𝜓)-weak contractive conditions, unique fixed point and some coincidence point results have been studied in the context of cone 2- metric spaces. Also, our obtained results generalize some results from cone metric space to cone 2-metric space. For the authenticity of the presented work, a non trivial example is also provided.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.293-306
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• 2022

In the present paper, we introduce the notation of 𝛿-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.233-247
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• 2022

In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, d_b). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권1호
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• pp.1-13
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• 2023

In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1097-1113
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• 2023

In this paper, we extend some fixed point theorems in rectangular b-metric spaces using subadditive altering distance and establishing the existence and uniqueness of fixed point for Hardy-Roger type mappings. Our result generalizes many known results in fixed point theory. Finally, we offer a example to illustrate our result.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.495-498
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• 2008

Every totally disconnected space is hereditarily disconnected. In this note, we provide an example of a hereditarily disconnected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

• 한국실내디자인학회논문집
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• 제17호
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• pp.203-209
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• 1998

Various living spaces have been attempted in modern resident life. basement and garre's function spaces are ignored even though they have essential environmental elements which are perceived instinctively by people. This is a good example of how rigid rough flows of interior space block the variety of living spaces. The primary purpose of this paper is to show the way of linking between whole living spaces and its parts to make better practical use of our living spaces. And I try to find out what is the original concept of he basement and garret and its relation with our residence how we use then in these days and what is the good way of practical use as our part of living space.

• 한국재난정보학회 논문집
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• 제6권1호
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• pp.92-119
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• 2010

As the necessity to utilize deep-placed underground spaces is increasing, we have to seriously consider the safety problems arising from the U/G spaces which is a restricted environment. Due to the higher cost of land compensation for above ground area and environmental issues, the plan to utilize deep-placed U/G spaces is currently only being established for the construction of U/G road network and GTX. However it is also expected that the U/G spaces are to be used as a living space because of the growing desires to change the above ground areas into the environmentally green spaces. Accordingly it is necessary to protect the U/G environments which is vulnerable against desasters caused by fire, explosion, flooding, terrorism, electric power failure, etc. properly. We want to introduce the principles of the Quantitative Risk Assessment(QRA) method for preparedness against the desasters arising from U/G environments, and also want to introduce an example of QRA which was implemented for the GOTTHARD tunnel which is the longest one in Europe.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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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.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.315-327
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• 2010

We give a xed point approach to the generalized Hyers-Ulam stability of the cubic equation f(2x + y) + f(2x - y) = 2f(x + y) + 2f(x - y) + 12f(x) in non-Archimedean normed spaces. We will give an example to show that some known results in the stability of cubic functional equations in real normed spaces fail in non-Archimedean normed spaces. Finally, some applications of our results in non-Archimedean normed spaces over p-adic numbers will be exhibited.