Non-Archimedean geometries may, as the example indicates, have properties significantly different from Euclidean geometry. A sequence in is called an M -Cauchy sequence, if for each and there exists such that for all. In this paper we introduce the concept of fuzzy order -contractive mappings and give two fixed point theorems on ordered non-Archimedean fuzzy metric spaces for fuzzy order -contractive type mappings. Pacific Journal of Mathematics— Let be defined by andthen and. The generalization suggested by Kirk of Caristi's fixed point theorem [ 19 ] is well known. Let Open image in new window for all Open image in new window. Radu V: Some remarks on the probabilistic contractions on fuzzy Menger spaces. Let Open image in new window and Open image in new window.

After the definition of the concept of fuzzy metric space by some authors [1–3], then the triple is called a non-Archimedean fuzzy metric space.

After the definition of the concept of fuzzy metric space by some authors [1, non -Archimedean fuzzy metric space is itself a fuzzy metric space. After the definition of the concept of fuzzy metric space by some. Let X, M, ∗ be a non-Archimedean fuzzy metric space with a∗b ≥ max{a.

Letting Open image in new windowwe obtain that Open image in new window.

MathSciNet Google Scholar In what follows Open image in new window is nondecreasing, subadditive mapping i. Hence all conditions of Theorem 2. Cite article How to cite?

Definition 3.

Let (X,M,⋆) be a fuzzy metric space (or a. modifying a definition of fuzzy metric space given by Kramosil and Michalek, Examples of fuzzy metric spaces (Sapena, ) On non-Archimedean fuzz. In mathematics, an ultrametric space is a metric space in which the triangle inequality is strengthened to d (x, z) ≤ max { d (x, y), d (y, z) } {\displaystyle d(x,z)\leq \max \left\{d(x,y),d(y,z)\right\}} d(x,z)\leq\max\left\{d.

Sometimes the associated metric is also called a non-Archimedean metric or.

George A, Veeramani P: On some results in fuzzy metric spaces. By using this site, you agree to the Terms of Use and Privacy Policy.

This shows that the sequence Open image in new window is M -Cauchy. In this paper we introduce the concept of fuzzy order -contractive mappings and give two fixed point theorems on ordered non-Archimedean fuzzy metric spaces for fuzzy order -contractive type mappings.

Let Open image in new window and Open image in new window be coordinate-wise ordering, that is, Open image in new window and Open image in new window.

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Let be a continuous, nondecreasing function and let be a fuzzy order -contractive and nondecreasing mapping w.
Then, for given. If there exists such that. Gregori V, Sapena A: On fixed-point theorems in fuzzy metric spaces. Video: Non archimedean fuzzy metric spaces wiki 2 4 Convergence in a metric space and completeness An example of such a space is the p-adic numbers. |

By taking the limit as we obtain.

Fuzzy Sets and Systems46 1 — Fang JX: On fixed point theorems in fuzzy metric spaces.

The second sense of the term is the metric geometry over a non-Archimedean valued field[3] or ultrametric space. This process is experimental and the keywords may be updated as the learning algorithm improves.

In the present paper we provide two different kinds of fixed point theorems on ordered nonArchimedean fuzzy metric spaces. The reader is referred to the nice paper [ 20 ] for some discussion of Kirk's problem on an extension of Caristi's fixed point theorem.

Note that, Open image in new window but Open image in new window then Open image in new window is not nondecreasing.