Convergence results for Górnicki type contractive mapping in CAT(0) spaces

This article presents new existence and uniqueness results for a nonlinear mapping in CAT(0) spaces. We prove these results without the necessity of stringent conditions, which are usually imposed on the mapping. We also prove the \(\Delta\) $\mathrm{\Delta }$ -convergence and strong convergence results for the Ishikawa iterative method of the considered nonlinear mapping. Finally, we apply one of the results to obtain a solution of a nonlinear integral equation.