In this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations.

In this paper, as a weak form of paracompact and expandable spaces, β-paracompact spaces and β-expandable spaces are defined, respectively. Some fundamental properties of these spaces are given. Also, it is proved that every β-paracompact space is a β-expandable space and the relations between these spaces and some previously studied spaces are investigated.

We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities.

Fatimah et al. suggested different complement operations for N-soft sets. However, these operations do not comply with De Morgan's laws and double complementation law for N-soft sets. So we do not restate some classical theorems on topological spaces in the realm of N-soft sets. Besides, the mappings are a basic mathematical tool which is utilized in numerous areas of mathematics, other sciences, and their applications. But there is not any note on the mappings in the setting of N-soft set theory. To deal with these problems, firstly, we advance the concept of complement of an N-soft set and demonstrate that De Morgan's laws and double complementation law are satisfied in N-soft set theory according to this new definition. Then we present an idea of the N-soft mappings and investigate some of their properties. Also, we illustrate given properties with examples and counter examples. Finally, using the N-soft mappings, we describe a mathematical system design for diagnosing purpose of the Covid-19 disease.

First we introduce a new structure of uniform spaces, called se-uniform spaces, and provide some of their basic properties. Next, we present the notion of a soft E-distance in se-uniform spaces, which is a soft version of E-distance of Aamri and El Moutawakil [M. Aamri, D. El Moutawakil, Acta Math. Acad. Peadegog. Nyhazi., 20 (2004), 83-91]. Then, by using the soft E-distance, we establish some fixed soft element theorems for various mappings on se-uniform spaces, which are the main results of the paper. This is the first kind of such results in this direction.