New fixed point theorem on G-metric spaces via x-distance

The purpose of this paper is to guarantee the existence of new fixed point result for
ða; w; xÞG-contractive mapping in complete G-metric spaces via x-distances. Also,
we apply our results to the existence result of nonlinear matrix equation which is
studied by Gao (J Appl Math Comput 50:109–116, 2016). Finally, we apply our
results to prove the existence of Hermitian positive definite solutions for nonlinear
matrix equations with some examples and numerical experiments for our results.