• The Pure and Applied Mathematics
• /
• v.29 no.4
• /
• pp.293-306
• /
• 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
• /
• v.27 no.2
• /
• pp.233-247
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.30 no.1
• /
• pp.1-13
• /
• 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.

• Korean Journal of Mathematics
• /
• v.16 no.4
• /
• pp.495-498
• /
• 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.

• Korean Institute of Interior Design Journal
• /
• no.17
• /
• pp.203-209
• /
• 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.

• Journal of the Society of Disaster Information
• /
• v.6 no.1
• /
• pp.92-119
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.50 no.2
• /
• pp.315-327
• /
• 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.

• Korean Journal of Mathematics
• /
• v.30 no.4
• /
• pp.603-614
• /
• 2022

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in b-metric-like spaces, which remains an extended version of corresponding results in b-metric spaces and metriclike spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in b-metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in b-metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.595-619
• /
• 2022

The purpose of this paper is to introduce an iterative algorithm for approximating a solution of split equality variational inequality problem for pseudomonotone mappings in the setting of Banach spaces. Under certain conditions, we prove a strong convergence theorem for the iterative scheme produced by the method in real reflexive Banach spaces. The assumption that the mappings are uniformly continuous and sequentially weakly continuous on bounded subsets of Banach spaces are dispensed with. In addition, we present an application of our main results to find solutions of split equality minimum point problems for convex functions in real reflexive Banach spaces. Finally, we provide a numerical example which supports our main result. Our results improve and generalize many of the results in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.421-438
• /
• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.