17 research outputs found

    Generalization of the Banach contraction principle

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    We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.Comment: 6 page

    Nonlinear contraction in bb-suprametric spaces

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    We introduce the concept of bb-suprametric spaces and establish a fixed point result for mappings satisfying a nonlinear contraction in such spaces. The obtained result generalizes a fixed point theorem of Czerwik and a recent result of the author.Comment: 8 page

    Fixed point theorems for α\alpha--contractive mappings of Meir--Keeler type and applications

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    In this paper, we introduce the notion of α\alpha--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems

    Comment on “Perturbation Analysis of the Nonlinear Matrix Equation ”

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    We show that the perturbation estimate for the matrix equation due to J. Li, is wrong. Our discussion is supported by a counterexample

    Fixed point results in generalized suprametric spaces

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    We introduce the concept of generalized suprametric spaces, which subsumes some existing abstract metric spaces. Then, we show the existence of fixed points for maps satisfying nonlinear contractions involving either extended comparison or ρ\rho -subhomogeneous functions. This study was carried out in generalized suprametric spaces as well as partially ordered generalized suprametric spaces. Some related results in JS-metric spaces and in bb-suprametric spaces are improved or extended

    Étude des interactions hydrodynamiques entre particules et parois par la méthode des éléments de frontière

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    This thesis presents a numerical study of hydrodynamic interactions between particles and a plane wall in a Newtonian fluid, on the assumption of a small Reynolds number. The Stokes equations are first transformed in the classical form of a surface integral equation giving the stresses on a surface surrounding the fluid. We calculate in this way the forces and torques exerted on the particles. A preliminary study corresponds to the axisymmetric problem for a chain of spherical particles arranged as a line perpendicular to the wall and moving following this line in a fluid at rest. Then we study the general problem of non-spherical particles, for any position of the particles and with the possibility of a flow field far from the particles. For the axisymmetric case, the points of collocation (which are also the sites of the singularities of Stokes or ``Stokeslets'') are selected on the surfaces of the particles so that their relative distances are proportional to the distance between close surfaces. To treat the general case, we developed a computer code using the boundary element method (BEM). The stokeslets are distributed here so as to take into account the hydrodynamic interactions and geometrical complexity of the configurations. Indeed, the grid is adapted to the variation of the gradient of stresses so that the boundary areas submitted to a strong hydrodynamic interaction are refined. The technique of dynamic grid refinement which we developed allowed us to better detect the lubrication regions between particles and wall as well as the interactions between particles. The stresses were calculated in this way for new geometrical configurations. Finally, the linear relationships between the forces and torques exerted on the particles and their translation and rotation velocities are expressed by the ``grand resistance matrix'' (or of its inverse the ``grand mobilility matrix'') which is then introduced into the fundamental relation of dynamics. Integrating, we determine the trajectories of the particles in various configurations: when in sedimentation in a fluid at rest in the vicinity of a wall, or freely rotating in a given flow field...The method also makes it possible to obtain the velocity fields of the fluid under these conditions.Cette thèse présente une étude numérique des interactions hydrodynamiques entre des particules et une paroi plane dans un fluide Newtonien, dans l'hypothèse d'un petit nombre de Reynolds. Les équations de Stokes sont d'abord transformées sous la forme classique d'une équation intégrale de surface donnant les contraintes sur la surface entourant le fluide. Nous avons calculé ainsi les forces et les couples exercés sur les particules. Une étude préliminaire correspond au problème axisymétrique pour une chaîne de particules sphériques arrangées suivant une ligne perpendiculaire à la paroi et en mouvement suivant cette ligne dans un fluide au repos. Puis nous avons abordé le problème général de particules non sphériques, la position des particules étant quelconque et le fluide loin des particules pouvant être en écoulement. Pour le cas axisymétrique, les points de collocation (qui sont aussi les emplacements des singularités de Stokes ou ``stokeslets'') sont choisis sur les surfaces des particules de façon que leurs distance relatives soient proportionnelles à la distance entre surfaces proches. Pour traiter le cas général, nous avons mis au point un code de calcul utilisant la méthode des éléments de frontière (BEM). Les stokeslets sont ici répartis de façon à prendre en compte les interactions hydrodynamiques et la complexité géométrique des configurations. En effet, le maillage est adapté à la variation du gradient de contraintes de façon que les zones de la surface qui entrent en forte interaction hydrodynamique soient les plus raffinées. La technique de raffinement dynamique de maillages que nous avons mise au point nous a permis de mieux détecter les zones de lubrification entre particules et paroi ainsi que les interactions entre particules. Les contraintes ont ainsi été calculées pour de nouvelles configurations géométriques. Enfin, les relations linéaires entre les forces et couples qui s'exercent sur les particules et leurs vitesses de translation et rotation sont exprimées au moyen de la « grande matrice de résistance » (ou de son inverse la « grande matrice de mobilité ») qui est alors introduite dans la relation fondamentale de la dynamique. En intégrant, nous avons déterminé les trajectoires des particules dans diverses configurations: en sédimentation dans un fluide au repos au voisinage d'une paroi, tournant librement dans un écoulement donné, ... La méthode permet aussi d'obtenir les champs de vitesse du fluide dans ces conditions

    Global Attractivity Results on Complete Ordered Metric Spaces for Third-Order Difference Equations

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    We establish fixed-point theorems for mixed monotone mappings in the setting of ordered metric spaces which satisfy a contractive condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation where satisfies certain monotonicity conditions with respect to the given ordering. As an application of our obtained results, we present some iterative algorithms to solve a class of matrix equations. A numerical example is also presented to test the validity of the algorithms