In this manuscript, we study the notion of \(\theta \) -contraction in the framework of \((\alpha ,\eta )\) -complete rectangular-b-metric spaces and investigate its role in fixed-point theory. We introduce a new class of \(\theta \) -contractive mappings and establish existence and uniqueness fixed-point theorems under suitable conditions. The obtained results extend and generalize several well-known fixed-point principles in non-standard metric spaces. To demonstrate the applicability and strength of the developed theory, we provide illustrative examples, derive useful corollaries, and present an application to a class of nonlinear integral equations. These findings contribute to the ongoing development of fixed-point theory in generalized metric settings and open new directions for further research and applications in mathematics and related fields.
