Common positive solution of two nonlinear matrix equations using fixed point results

We discuss a pair of nonlinear matrix equations (NMEs) of the form (Formula presented), and the operators F, G: P(n) → P(n) are continuous in the trace norm. We go through the necessary criteria for a common positive definite solution of the given NME to exist. We develop the concept of a joint Suzuki-implicit type pair of mappings to meet the requirement and achieve certain existence findings under weaker assumptions. Some concrete instances are provided to show the validity of our findings. An example is provided that contains a randomly generated matrix as well as convergence and error analysis. Furthermore, we offer graphical representations of average CPU time analysis for various initializations.