On fixed points of rational contractions in generalized parametric metric and fuzzy metric spaces

Abstract

Abstract We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for ( α , ψ ) $(\alpha ,\psi )$ -rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for ( α , ψ ) $(\alpha , \psi )$ -rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces.

Keywords

• Fixed point
• α-admissible
• ( α , ψ ) $(\alpha , \psi )$ -rational contraction
• Generalized parametric metric spaces
• Fuzzy metric spaces