For vector-valued functions,the notion of transfer cone semicontinuity of one vector-valued function with respect to another vector-valued function and cone -θ-quasiconcavity are introduced.we prove the existence theorem for vector equilibrium problem relative to the vector-valued functions with weak continuity,weak convexity and without compactness of the space and offer its equivalent maximal version.As applications,we obtain some existence theorems of vector equilibrium problems and real-valued quilibrium problems,while some new fixed point theorems are proved.Our results include some corresponding results in the literatures as special cases.
We consider random walk in random environment on Z~d(d≥1) and prove the Strassen' s strong invariance principle for this model,via martingale argument and the theory of fractional coboundaries of Derriennic and Lin,under some conditions which require the variance of the quenched mean has a subdiffusive bound.
We consider the Bernoulli first-passage percolation on Z~d(d≥2).That is,the edge passage time is taken independently to be 1 with probability 1 - p and 0 otherwise.Letμ(p) be the time constant.We prove in this paper thatμ(p_1)-μ(p_2)≥μ(p_2)/(1-p_2)(p_2-p_1) for all 0≤p_1 < p_2 < 1 by using Russo's formula.
