Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping

Abstract

In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone metric spaces, they are the same. Additionally, we prove some fixed point theorems related to diametrically contractive mapping in a complete soft cone metric space.

A Soft Set Approach to Relations and Its Application to Decision Making

“…After Maji et al [10] and Ali et al [11] laid the foundations of the soft set operations, different interpretations have emerged about extending mathematical structures to the soft set theory (See [12][13][14][15][16][17][18], and others in them). The soft elements and elementary (ε-) soft set operations were brought forward by Das and Samanta [19], and some mathematical structures have been examined using these concepts by several authors [20][21][22][23][24][25][26][27].…”

On elementary soft compact topological spaces

“…by using the notion of soft element [18][19][20]. Also, works on fixed point theory have been ongoing over the soft sets, the soft metrics and soft cone metrics [21][22][23][24][25][26]. In recent years some authors studied on 𝜖-soft topological spaces by using elementary operations on soft sets [27][28][29][30][31].…”