Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

Abstract

The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics. 
 Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studied and some essential theorems are proved.

Fixed Point Results for Almost Contraction Mappings in Fuzzy Metric Space

“…At the end of the paper, some examples are given to support the results. A large number of papers on 𝐹ℳ-space have been published; see [6][7][8][9] . Beginning with the specification of 𝐹ℳ-space, Sihag et al 10 .…”

Some Results of Fixed Point for Single Value Mapping in Fuzzy Normed Space with Applications

“…On other hand, functional analysis is one of the most important areas of contemporary mathematics. It plays an essential role In the theory of differential equations, representation theory, and probability, as well as in the study of many different properties of different spaces, such as metric space, Hilbert space, Banach space, and others see [2][3][4][5][6][7][8]. Zadeh [9] presented the ingenious notion of a fuzzy set in his renowned paper, many mathematicians became aware of the myriad possibilities for expanding the classical conclusions in the new fuzzy framework and of their countless applications.…”

“…Following this, the notion of fuzzy metric space is modified by George and Veeramani [11]. There have been several papers pertaining to fuzzy metric spaces see [12][13][14]. Katsaras [15] was the first to propose the concept of fuzzy norms in linear spaces.…”

Best Proximity Point Theorem for α ̃–ψ ̃-Contractive Type Mapping in Fuzzy Normed Space

“…George and Veeramani 3 modified the notion of fuzzy metric spaces. A wide number of works have been published in fuzzy metric spaces; see [4][5][6][7] . Katsaras A, 8 was the first to establish the fuzzy norm on a linear space.…”