New fixed point theorem on G-metric spaces via \(\omega\)-distance

The purpose of this paper is to guarantee the existence of new fixed point result for \((\alpha ,\psi ,\omega )_G\) ${(\alpha ,\psi ,\omega )}_G$ -contractive mapping in complete G-metric spaces via \(\omega\) $\omega$ -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.