Convergence in \(\varphi \)-variation for Mellin-type nonlinear integral operators

In the present paper, we examine Mellin-type nonlinear integral operators equipped with the Haar measure. Using \(\varphi \) $\phi$ -absolutely continuous functions, we obtain some approximations via summability process. Order of convergence is also observed. In addition, we have a general characterization theorem for \(\varphi \) $\phi$ -absolutely continuous functions. Finally, we give an application of our study with some illustrations and numerical computations.