On Fixed Point Theorem in Fuzzy Normed Space

Abstract

The formal balls in fuzzy normed space (characterized by closed balls in) are ordered by reverse inclusion depending on the concept of level sets. The set of formal balls in a fuzzy normed space is called a fuzzy domain normed space denoted by. This set is directed complete partially ordered set (dcpo), its maximal elements are the suprema. A contraction mapping principle is defined on. Banach fixed point theorem is studied and proved on .

Another Type of Fuzzy Inner Product Space

“…Raghad [7] introduced some types of fuzzy convergence sequences of operators that are defined on a standard fuzzy normed space and investigated some properties and relationships between these concepts. Authors in [8][9][10] proved some results about the ISSN: 0067-2904 best proximity point theorem and fixed point theorem in fuzzy normed spaces. J. R.Kider and M. N. Gheeab [11] introduced the definition of a general fuzzy normed space as a generalization of the notion of fuzzy normed space after that they investigated and proved the basic properties of this space.…”

Best Proximity Point Theorem for φ ̃–ψ ̃-Proximal Contractive Mapping in Fuzzy Normed Space

“…On the other hand, Katsaras [2] was a pioneer in establishing fuzzy norms in linear spaces. Numerous articles on fuzzy normed spaces have been published; see [3][4][5][6][7][8][9]. In this paper, the notion of 𝜑 ̃-𝜓 ̃− proximal contractive mapping (briefly, 𝜑 ̃-𝜓 ̃− 𝑃𝐶 mapping) in a fuzzy normed space is presented, as well as the proof of the best proximity point theorem for this mapping.…”