We present a new sufficient semilocal convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in cases not covered in other studies such as Dennis (1971) [12], Ezquerro et al. (2000, 2010) [13,14], Kornstaedt (1975) [18], Potra and Ptak (1984) [24], Potra (1985, 1979, 1982, 1981, 1984) [23,25,26,27,28], Proinov (2010) [29], Schmidt (1978) [31] or Yamamoto (1987) [32]. The advantages of our approach also include a tighter convergence analysis under the same computational cost. Applications, where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also given in this study. (C) 2014 Elsevier Inc. All rights reserved.