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Öğe Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations(SHANGHAI UNIV, 2007) Kutukcu, Servet; Tuna, Adnan; Yakut, Atakan T.Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.Öğe On the Schlafli differential formula based on edge lengths of tetrahedron in H-3 and S-3(SPRINGER, 2009) Yakut, Atakan T.; Savas, Murat; Kader, SerkanWe obtain a new version of Schlafli differential formula based on edge lengths for the volume of a tetrahedron in hyperbolic and spherical 3-spaces, by using the edge matrix of a hyperbolic( or spherical) tetrahedron and its submatrix.Öğe Orthogonal Projections Based on Hyperbolic and Spherical n-Simplex(HINDAWI PUBLISHING CORP, 2015) Savas, Murat; Karliga, Baki; Yakut, Atakan T.Orthogonal projection along a geodesic to the chosen k-plane is introduced using edge and Gram matrix of an n-simplex in hyperbolic or spherical n-space. The distance from a point to k-plane is obtained by the orthogonal projection. It is also given the perpendicular foot from a point to k-plane of hyperbolic and spherical n-space.Öğe Vertex angles of a simplex in hyperbolic space Hn(Springer, 2006) Karliga, Baki; Yakut, Atakan T.For an n-simplex in H-n or S-n, we give sine theorems and their results for kth-order vertex angles which are defined in this paper. The Gram and edge matrices, and polar simplex of n-simplex in H-n or S-n are used to prove the theorems and their results.
