Under the assumption of known root multiplicity m is an element of N, a triparametric family of two-point optimal quartic-order methods locating multiple zeros are investigated in this paper by introducing a weight function dependent on a function-to-function ratio. Special cases of weight functions with selected free parameters are considered and studied through various test equations and numerical experiments to support the theory developed in this paper. In addition, we explore the relevant dynamics of proposed methods via Mobius conjugacy map when applied to a prototype polynomial (z - a)(m)(z - b)(m). The results of such dynamics are visually illustrated through a variety of parameter spaces as well as dynamical planes. (C) 2017 Elsevier Inc. All rights reserved.