Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 28 num. 2 lang. es <![CDATA[SciELO Logo]]> <![CDATA[<b><i>θ</i></b><b>-GENERALIZED SEMI-OPEN AND <i>θ</i>-GENERALIZED SEMI-CLOSED FUNCTIONS</b>]]> In this paper, we introduce and study the notions of θ-generalized-semi-open function, θ-generalized- semi-closed function,pre θ-generalized-semi-open function,pre θ-generalized-semi-closed function, contra pre θ-generalized-semi-open, contra pre θ-generalized-semi-do sed function and θ-generlized-sem-homeomorphism in topological spaces and study their properties. <![CDATA[<b>ON EXISTENCE OF PERIODIC SOLUTION TO CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS</b>]]> In this paper, it is investigated the existence of periodic solutions to the nonlinear third order differential equation : x'" + c2(t)x" + c1(f)x' + f(t, x) = p(t, x, x', x"). The Leray-Schauder principle is used to show the existence of periodic solutions of this equation. <![CDATA[<b>SCHUR RING AND QUASI-SIMPLE MODULES</b>]]> Let R be a ring of algebraic integers of an algebraic number field F and let G ≤ GLn(R) be a finite group. In this paper we show that the R-span of G is just the matrix ring Mn(R) of the n X n-matrices over R if and only if G/Opi(G) is absolutely simple for all p i ∈ π, where π is the set of the positive prime divisors of |G| and Opi(G) is the largest normal pi-subgroup. <![CDATA[<b>DISQUES J-HOLOMORPHES CONTENUS DANS UNE HYPERSURFACE</b>]]> We study germs of J-Holomorphic curves contained in M, a real analytic hypersurface of an symplectic manifold of dimension 4- We show, under topological hypothesis on M, that if M is compact then M is of finite type and so there is no germs of J-holomorphic curves on M (with J adapted with the symplectic form). In C² with the standard complex structure, this is a classical result of Diederich-Fornaess. <![CDATA[<b>ON THE LOCAL CONVERGENCE OF A MIDPOINT METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION</b>]]> In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorably with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided. <![CDATA[<b>INCLUSION RELATIONS FOR K-UNIFORMLY STARLIKE FUNCTIONS AND SOME LINEAR OPERATOR</b>]]> In this paper, we have established the inclusion relations for k-uniformly starlike functions under the Ls (ai)f(z) operator. These results are also extended to k- uniformly convex functions, close to convex and quasi-convex functions. <![CDATA[<b>PRODUCTS OF <i>L</i>F-TOPOLOGIES AND SEPARATION IN <i>L</i>F-TOP</b>]]> For a GL-monoid L provided with an uniform structure, we build an LF-topology on the cartesian product of a family of LF-topological spaces. We also show that the product of an arbitrary family of Kolmogoroff (Hausdorff) LF-topological spaces is again a Kolmogoroff (Hausdorff) LF-topological space.