Common Fixed Point Theorems in Complex-Valued Non-Negative Extended b-Metric Spaces

Abstract

We introduce complex valued non-negative extended b-metric spaces and establish new fixed point results for mappings under some rational contractions. Our idea improves and extends corresponding fixed point theorems in the setting of b-metric, extended b-metric and classical metric spaces. Nontrivial examples are provided to support the hypotheses and usefulness of the main result obtained herein. Motivated by the ideas presented in [3, 8, 21], we introduce the concept of complex valued non-negative extended b-metric spaces and establish new fixed point theorems for mappings under some rational contractive inequalities. Our idea improves and extends the above mentioned articles and a few others in the corresponding literature. Nontrivial examples are provided to indicate the usefulness and validity of the main result obtained herein