Fixed point of hardy-rogers contraction mappings in non-solid cone \(\chi_b\)-metric space with applications

Abstract

The concept of cone χ_b-metric spaces was recently introduced in 2023 as a generalization of both cone metric spaces and traditional χ-metric spaces, allowing for the possibility that the underlying cones are non-solid. The main objective of this article is to establish certain fixed point results for Hardy–Rogers-type mappings and to investigate the T-stability of Picard’s iteration in the framework of non-solid cone χ_b-metric spaces. As an application, we employ the main results to demonstrate the existence and uniqueness of solutions to a nonlinear integral equation.