Scielo RSS http://www.scielo.cl/rss.php?pid=0716-091720130001&lang=pt vol. 32 num. 1 lang. pt http://www.scielo.cl/img/en/fbpelogp.gif http://www.scielo.cl http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100001&lng=pt&nrm=iso&tlng=pt We propose a geometric proof of the fundamental Lelong-Poincaré formula : dd c log |/ | = [/ = 0] where f is any nonzero holomorphic function defined on a complex analytic manifold V and [/ = 0] is the integration current on the divisor of the zeroes of /. Our approach is based, via the local parametrization theorem, on a precise study of the local geometry of the hypersurface given by /. Our proof extends naturally to the meromorphic case. http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100002&lng=pt&nrm=iso&tlng=pt Using the alternative fixed point theorem, we establish the generalized Hyers-Ulam-Rassias stability of a Cauchy type functional equation for functions taking values in arbitrary complete (real or complex) â-normed spaces. http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100003&lng=pt&nrm=iso&tlng=pt One of the most efficient methods of obtaining information on the behaviour of solutions of difference equations, even when they cannot be solved explicitly, is the comparison principle. In general, the comparison principle is concerned with estimating a function satisfying adifference inequality by the solution of the corresponding difference equation. In the present paper, we shall establish various forms ofthe principle for fractional order difference equations. http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100004&lng=pt&nrm=iso&tlng=pt In this paper, the notion of generalized preopen compactness is introduced and connections to other several types of compactness are discussed. In addition, new separation axioms are established. http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100005&lng=pt&nrm=iso&tlng=pt We prove an extension of a classical result for null controllability of linear control systems on Euclidean spaces, to linear control systems on a connected Lie group G, assumed to be simply connected and nilpotent. http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172013000100006&lng=pt&nrm=iso&tlng=pt We present a tighter than before semilocal convergence analysis for the two-step Newton method of order three using recurrent functions. Numerical examples are also provided to show that our convergence criteria are satisfied but earlier studies such as in nine,thirteen,fifteen are not satisfied.