A Fixed-Point Chatterjea–Singh Mapping Approach: Existence and Uniqueness of Solutions to Nonlinear BVPs

This paper introduces an application of the Chatterjea–Singh fixed-point theorem to nonlinear boundary value problems (BVPs). We define a Chatterjea–Singh mapping as one whose iterate Tp satisfies a Chatterjea-type contractive condition. Under this weaker assumption than classical Banach or Chatterjea contractions, we prove the existence and uniqueness of solutions to second-order BVPs. Our method applies even when T itself does not satisfy a contraction property. Examples illustrate how iteration can recover convergence where standard conditions fail. This work extends generalized fixed-point theory in differential equations and highlights the flexibility of delayed contraction criteria.