Parida, P. K.P. K.ParidaGupta, D. K.D. K.Gupta2025-08-302025-08-302010-12-0110.1080/002071609030266262-s2.0-78649901916https://d8.irins.org/handle/IITG2025/21083The aim of this paper is to establish the semilocal convergence of a family of third-order Chebyshev-type methods used for solving nonlinear operator equations in Banach spaces under the assumption that the second Frechet derivative of the operator satisfies a mild ω-continuity condition. This is done by using recurrence relations in place of usual majorizing sequences. An existence-uniqueness theorem is given that establishes the R-order and existence-uniqueness ball for the method. Two numerical examples are worked out and comparisons being made with a known result. © 2010 Taylor & Francis.falseω-continuity condition | nonlinear operator equations | R-order of convergence | recurrence relations | semilocal convergenceArticle102902653405-3419December 201023arJournal17