Fixed-Point Results for Interpolative t-Simulation and Interpolative Kannan-Type Contractions with Applications

This paper investigates interpolative contractive mappings in two different settings. In the first part, we establish existence and uniqueness results for fixed points of the existing interpolative Kannan-type contraction in complete extended b-metric spaces. The theoretical developments are further validated through illustrative examples together with an application. In the second part, we introduce a new class of interpolative t-simulation contractions in complete metric spaces and derive fixed-point theorems for orbitally continuous self-mappings. To demonstrate the usefulness of the proposed framework, we apply the obtained results to a nonlinear Fredholm integral equation. The established theorems generalize and strengthen several well-known fixed-point results, highlighting the versatility and applicability of interpolative techniques in both metric and generalized metric spaces.