This paper studies the proximal point algorithm for class of generalized variational inequalities. By using upper semicontinuity result establishing weakly univalent operators, we show that iterative sequence generated by is bounded, approaches to solution set initial problem, and each its accumulation points a provided bounded. We also give an example necessity boundedness.

In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems i...

We investigate the continuity of equilibrium in differential information economies with a finite number of agents. In this setting, agents can make contingent contracts based on events that are commonly observed. With private information modeled as finite partitions of a compact and metrizable space of states of nature, we introduce a topology on information that evaluates the similarity betwee...

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both pertur...

Under new assumptions, we provide suffcient conditions for the upper and lower semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010 . Some examples a...

We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper semicontinuity which plays the role of convexity, and allows to prove a radial representation result for nonconvex functions. An application to the relaxation of ...

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation −∆ut + α ∆ut + μ∆ u+∇ · −→ F (u) +B(u, u) = ǫg(x, t). Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor {Aǫ(t)}t∈R of the equation with ǫ > 0 converges to the global attract...