| Summary: | In this paper, we introduce a new class of mappings called “generalized <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding.
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