This paper discussed normed, cone normed, 2-normed, and cone 2-normed spaces. Then constructed some orthogonalities in cone 2-normed spaces, especially for ℓ 2 space.

In this paper, we explore two properties of cone rectangular metric spaces: completeness and fixed point theorem. We analyse sufficient condition and necessary requirement for a cone rectangular metric space to be complete. We also give a new proof for fixed point theorem in cone rectangular metric spaces.

In this paper we study boundedness and continuity of linear operator on cone normed space by showing that a linear mapping from cone normed space ′ [ , ] to [ , ] is continuous and bounded. Moreover, we study a set of bounded linear operator on cone normed space which is a cone Banach space. By means, we show that the cone Banach space is complete with its cone norm.

In this paper, we generalized concept of metric space, namely the type-metric space. The difference between type-metric with metric is triangular inequalities. We will investigate some properties of the convergent sequence, the Cauchy sequence, the contractive sequence on the type-metric space. Then, we investigate the relationship between the metric space and the type-metric space with an the example. At the end of this paper, we construct a type-metric function on the cone metric space.

Tsunamis are disasters that cause so much damage. In the history of the tsunami, Indonesia has been hit by tsunami several times, based on data from the National Disaster Management Agency (BNBP), as of 1629 - 2007, Indonesia was recorded 184 times affected by large and small tsunami disasters. Based on these data, it is very important for Indonesia to increase security against the tsunami disaster. Also, the tsunami in Indonesia occurred due to earthquakes, volcanic eruptions, and landslides in the sea. This study discussed about to the tsunami with a location located in the southern of Java, precisely in the area of Central Java, considering that in 2017 there was friction between the Indies and Eurasian plates which caused an earthquake measuring 6.9 magnitude, but did not cause a tsunami. In this study, a tsunami wave propagation simulation was carried out with the aim of knowing how long it would take the waves to the shoreline and how high the waves would be when they were on the shoreline. The model used is a tsunami model created by Imamura by solving differential equations using finite difference and Runge-Kutta 4th order. Based on the simulation results with the initial determination of a 5 m tsunami wave centered at a distance of 25 km from the shoreline, Tsunami waves with a height of 8.7 m will arrive at the shoreline at 140 seconds. With wave height is 8.7 m at the shoreline, the water will enter the land or can also be called the tsunami disaster. At that time, residents are expected to have been evacuated from the coastal area. In addition, based on numerical simulations that have been carried out, information is obtained that the computation time of the method is faster than the computation time of the Runge-Kutta method with differences in altitude results that are quite small and can be tolerated. This shows that the Finite Difference method can be applied to tsunami disaster mitigation software because it has a fairly fast computing time compared to the Runge-Kutta 4th order method.