Asian Research Journal of Mathematics

This study establishes fixed point results for expansive self-maps in complete extended b-metric spaces, where the multiplicative factor in the triangle inequality is governed by a variable control function. Because repeated use of the extended triangle inequality can amplify orbitwise distances, the analysis incorporates an orbit-bound condition, or an analogous summability requirement, to control the distortion generated by backward preimage iterations. Under surjectivity and suitable expansive inequalities, existence and uniqueness results are developed for a single mapping, a two-term condition, a multi-term coefficient condition, and a pair of mappings with a common fixed point. The proofs construct preimage sequences and show geometric decay of successive gaps; completeness then yields convergence, while the expansive conditions establish the fixed-point property and uniqueness. Several examples of extended b-metric spaces are provided to illustrate the framework. A numerical example based on an affine map demonstrates the convergence of the backward sequence towards its analytic fixed point. The manuscript further considers an affine scaling-plus-bias operator in a finite-dimensional setting and relates its equilibrium to the proposed expansive fixed point framework under the stated boundedness, invertibility, and orbit conditions. Overall, the results extend the manuscript’s expansive-mapping analysis from metric and b-metric settings to the extended b-metric setting while retaining explicit control of the variable distortion.