Permutation Contractions in Complete b-Metric Spaces: Fixed Point Results and Applications

Permutation contractions have recently been investigated as a flexible generalization of classical contractive conditions through suitable combinations of orbit distances. In this paper, we study permutation contractions on a complete b-metric space and establish a generalized Banach-type fixed point theorem ensuring the existence and uniqueness of a fixed point. We further derive a per-term dominated version in which each orbital distance is controlled by the base distance, leading to a global contractive condition and a corresponding fixed point theorem. As a consequence, suitable Kannan- and restricted Hardy–Rogers-type fixed point results are obtained under additional assumptions. To illustrate the applicability of the theoretical results, we apply the obtained fixed point principles to prove the existence and uniqueness of solutions of a linear system of equations and to the existence of a solution for a second-order boundary value problem. These results demonstrate that permutation contractions provide a flexible framework for extending fixed point techniques in b-metric spaces.