Abstract
We present some topics about random spaces. The main purpose of this paper is to study topological structure of random normed spaces and random functional analysis. These subjects are important to the study of nonlinear analysis in random normed spaces.
Highlights
The purpose of this paper is to give a comprehensive text to the study of nonlinear random analysis such as the study of fixed point theory, approximation theory and stability of functional equations in random normed spaces
We extended definitions and results on the triangular norm on lattices
Note that, when M contains only the two points 0 and 1, A is nonfuzzy and λA w is identical to the characteristic function of a non-fuzzy set
Summary
The purpose of this paper is to give a comprehensive text to the study of nonlinear random analysis such as the study of fixed point theory, approximation theory and stability of functional equations in random normed spaces. The notion of random normed space goes back to Sherstnev 1 and Hadzic 2–4 who were dulled from Menger 5 , and Schweizer and Sklar 4 works. Some authors 6–11 considered some properties of probabilistic normed and metric spaces fuzzy metric and normed spaces 12–21. Fixed point theory 3, 22– 26 , approximation theory 27–31 , and stability of functional equations 32–38 are studied at random normed space and its depended space that is, fuzzy normed space. Ii Topological structure of random normed spaces. Iv Relationship between random normed spaces and fuzzy normed spaces I Basic theory of triangular norms. ii Topological structure of random normed spaces. iii Random functional analysis. iv Relationship between random normed spaces and fuzzy normed spaces
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