On solving variational inequalities defined on fixed point sets of multivalued mappings in Banach spaces

AbstractWe are concerned with the problem of solving variational inequalities which are defined on the set of fixed points of a multivalued nonexpansive mapping in a reflexive Banach space. Both implicit and explicit approaches are studied. Strong convergence of the implicit method is proved if the space satisfies Opial's condition and has a duality map weakly continuous at zero, and the strong convergence of the explicit method is proved if the space has a weakly continuous duality map. An essential assumption on the multivalued nonexpansive mapping is that the mapping be single valued on its nonempty set of fixed points

Remarks on multivalued nonexpansive mappings

Convergence of fixed point sets of multivalued nonexpansive mappings is studied under both the Mosco and Hausdorff senses. A characterization for *- nonexpansive multivalued mappings is given. Also a counterexample is constructed to show a negative answer to a question raised by A. Canbtti, G. Marino and P. Pibtramala.Dirección General de Investigación Científica y TécnicaJunta de Andalucí

Rayleigh-Benard Simulation using Gas-Kinetic BGK Scheme in the Incompressible Limit

In this paper, a gas-kinetic BGK model is constructed for the Rayleigh-Benard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times and pseudo-temperature in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr=1 in the original BGK model. The 2D Rayleigh-Benard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results

On Property (M) and Its Generalizations

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Qualitative and quantitative properties for the space ℓp,q

The space lp,q is simply the space lp but renormed by 1 Ixlp,q =(11x+llg + IIx-IIg);, ß E where II'[Ip is the usual lp norm and x + and x- are the positive and negative. parts of x, respectively. Bynum used lp,1 and Smith and Turett used 12,1 to show that neither normal structure nor uniform normal structure is a self dual property for Banach spaces. In this paper we present some more qualitative and quantitative properties for Ip,q; in particular, we provide an affirmative answer to a question of Khamsi.Dirección General de Investigación Científica y TécnicaJunta de Andalucí

A compactness result for differentiable functions with an application to boundary value problems

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