Abstract

In this paper, we introduce the notion of orthogonal relation on a soft set $(F,A)$ and some related concepts. This notion allows us to consider fixed point theorem in SO-complete instead of complete soft metric spaces introduced by Yazar et.al. (Filomat 30:2 (2016), 269--279). Then, the existence and uniqueness of soft fixed points for a generalized soft contractive mapping are proved. Also, some examples are given to support that our main theorem is a real extension of Yazar et.al.

Keywords: Soft metric space; soft fixed point; orthogonal set; Picard operator.

MSC: 34A12, 65R10, 65R20

Pages:  187$-$195     

Volume  72 ,  Issue  3 ,  2020