Applications of fixed point theorems in extended cone $b$-metric spaces over Banach algebras to integral equations arising in signal processing

The aim of this research article is to explore the notion of extended cone $b$-metric spaces over Banach algebras and to establish new fixed point theorems for both single-valued mappings and multi-valued mappings. These results extend and generalize several well-known findings in metric fixed point theory. To demonstrate the applicability of our theoretical results, we provide illustrative examples that highlight the distinct features of our approach. Additionally, we showcase the practical relevance of our primary theorem by solving a Fredholm integral equation of the second kind, which arises in the context of radar and sonar signal processing.