Mathematical analysis

Generalization

Injective metric space

Programming language

Artificial intelligence

Fixed-point theorem

Contraction mapping

Metric space

Pure mathematics

Mathematics

Contraction principle

Computer science

Extension (predicate logic)

Fixed point

Discrete mathematics

Fuzzy logic

Numerical Methods for Partial Differential Equations

In this paper, we introduce a new extension in the subject of fuzzy metric, called controlled fuzzy metric space. This notion is a generalization of fuzzy b‐metric space. Also, we prove a Banach‐type fixed point theorem and a new fixed point theorem for some self‐mappings satisfying fuzzy ψ ‐contraction condition that is more general than existing theorems. Furthermore, we establish some examples about our main results.

Controlled fuzzy metric spaces and some related fixed point results