Parida, P. K.P. K.ParidaGupta, D. K.D. K.Gupta2025-08-302025-08-302009-06-2510.1142/S02198762090018382-s2.0-67549104451https://d8.irins.org/handle/IITG2025/21116The aim of this paper is to discuss the convergence of a third order method for solving nonlinear equations F(x)=0 in Banach spaces by using recurrence relations. The convergence of the method is established under the assumption that the second Fréchet derivative of F satisfies a condition that is milder than Lipschitz/Hölder continuity condition. A family of recurrence relations based on two parameters depending on F is also derived. An existence-uniqueness theorem is also given that establish convergence of the method and a priori error bounds. A numerical example is worked out to show that the method is successful even in cases where Lipschitz/Hölder continuity condition fails. © World Scientific Publishing Company.falseω-continuous | a priori error bounds | Banach spaces | Recurrence relations | Third order methodArticle291-30620092arJournal1