Continuous controlled cone metric-type spaces over real Banach algebras and fixed-point results

In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type space. We introduce a new metric space and prove analogs of Banach-, Kannan- and Reich-type fixed-point theorems. We also furnish various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in the literature.

Automated summary

In this article, a new geometrical structure that combines a cone metric space over Banach algebra and a controlled metric-type space is introduced. A new metric space is proposed, and analogs of Banach-, Kannan- and Reich-type fixed-point theorems are proved. Various concrete examples are provided to validate the results, which generalize many well-known results in the literature.