In this paper, a new class of contractive mappings, called E-Rakotch contractions, is introduced and studied in the setting of equivalent-distance spaces. The notion is formulated by combining Rakotch’s variable coefficient contraction with the \(E_{A, B}\) -distance framework, which has recently been employed to unify several generalized metric structures. A fixed point theorem is established to ensure the existence, uniqueness, and global convergence of the Picard iteration for E-Rakotch contractions on complete metric spaces. The classical Rakotch contraction principle is extended and recovered as a special case of the obtained result. Several examples are provided to illustrate the new concept, including mappings arising from equivalent metrics and nonlinear rational functions. Applications are further presented to a nonlinear algebraic equation, a Volterra integral equation of the second kind, and a schematic fractional differential equation.
