A soft version of the Knaster–Tarski fixed point theorem with applications

Abstract

In this paper first we define a partial order on a soft set (F, A) and introduce some related concepts. Then using the concept of a soft mapping introduced by Babitha and Sunil [Comput. Math. Appl., 60 (7) (2010), 1840-1849], a soft version of Knaster-Tarski fixed point theorem is obtained. Some examples are presented to support the concepts introduced and the results proved herein. As an application of our result, we show that the soft Knaster-Tarski fixed point theorem ensures the existence of a soft common fixed point for a commuting family of order-preserving soft mappings.

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].…”