Abstract
We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.
Highlights
In recent years, the fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering
Fuzzy set theory is a powerful hand set for modelling uncertainty and vagueness in various problems arising the field of science and engineering
The fuzzy topology 4–8 proves to be a very useful tool to deal with such situations where the use of classical theories breaks down
Summary
The fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. Quite recently the concepts of l-intuitionistic fuzzy compact set and strongly intuitionistic fuzzy uniformly convex normed space are studied, and Schauder fixed point theorem in intuitionistic fuzzy normed space is proved in 30. A binary operation ∗ : 0, 1 × 0, 1 → 0, 1 is said to be a continuous t-norm if it satisfies the following conditions:. Using the notions of continuous t-norm and t-conorm, Saadati and Park 10 have recently introduced the concept of intuitionistic fuzzy normed space as follows. The five-tuple X, μ, υ, ∗, ♦ is said to be intuitionistic fuzzy normed spaces for short, IFNS if X is a vector space, ∗ is a continuous t-norm, ♦ is a continuous t-conorm, and μ, υ are fuzzy sets on X × 0, ∞ satisfying the following conditions. The concepts of convergence and Cauchy sequences in an intuitionistic fuzzy normed space are studied in 10. 1.4 for all x, y ∈ X, for all t ∈ R
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