On a bilinear operator free third order method on Riemannian manifolds

We present a semilocal convergence analysis of a bilinear operator free third order method on Riemannian manifolds. Using a combination of generalized Lipschitz and center-Lipschitz conditions, we provide a convergence analysis which expands the applicability of the method even in the setting of nonlinear equations considered in earlier studies such as (cf. [4,9,38]).