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An efficient family of two-point derivative free methods with memory for solving nonlinear equations is presented. It is proved that the convergence order of the proposed family is increased from 4 to at least 2 + √ 6 ≈ 4.45, 5, 1 2 5 + √ 33 ≈ 5.37 and 6, depending on the accelerating technique. The increase of convergence order is attained using a suitable accelerating technique by varying a free parameter in each iteration. The improvement of convergence rate is achieved without anydoi:10.2298/aadm110905021p fatcat:zbv2td7clzaqpiietwoz3kxnra