In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a...In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.展开更多
We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results pres...We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.展开更多
Let X be a C^(1+)vector field on a compact Riemannian manifold M with dimension d≥3.LetΛbe a transitive singular hypebolic set with positive volume.We show thatΛ=M andΛis a uniformly hyperbolic set without singula...Let X be a C^(1+)vector field on a compact Riemannian manifold M with dimension d≥3.LetΛbe a transitive singular hypebolic set with positive volume.We show thatΛ=M andΛis a uniformly hyperbolic set without singularities.展开更多
文摘In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm.
基金King Fahd University of Petroleum and Minerals for supporting the research project IN121055Higher Education Commission (HEC) of Pakistan for financial support
文摘We introduce a one-step implicit iterative method for two finite families of asymptotically nonexpansive mappings in a hyperbolic space and use it to approximate common fixed points of these families. The results presented in this paper are new in the setting of hyperbolic spaces. On top, these are generalizations of several results in literature from Banach spaces to hyperbolic spaces. At the end of the paper, we give an example to validate our results.
基金support of Shanghai Key Laboratory of Pure Mathematics and Mathematical Practicethe Project funded by China Postdoctoral Science Foundation(Grant No.2020TQ0098)。
文摘Let X be a C^(1+)vector field on a compact Riemannian manifold M with dimension d≥3.LetΛbe a transitive singular hypebolic set with positive volume.We show thatΛ=M andΛis a uniformly hyperbolic set without singularities.
