in this paper, we establish some results on the existence of at least three weak solutions for adirichlet problem involving p-laplacian using a variational approach.

In the present paper, a new generalization of Browder fixed point theorem is obtained. As its applications, we obtain some generalized versions of Browder’s theorems for quasi-variational inequality and Ky Fan’s minimax inequality and minimax principle.

Function estimation over the Besov spaces under pointwise r (1 ≤ r < ∞) risks is considered. Minimax rates of convergence are derived using a constrained risk inequality and wavelets. Adaptation under pointwise risks is also considered. Sharp lower bounds on the cost of adaptation are obtained and are shown to be attainable by a wavelet estimator. The results demonstrate important differences b...

In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general s...

In this work we obtain two minimax inequalities in G-convex spaces which extend and improve a large number of generalizations of the Ky Fan minimax inequality and of the von Neumann–Sion minimax principle. © 2005 Elsevier Ltd. All rights reserved.

We investigate the possibility of finding multi-purpose nonparametric function estimators that are minimax rate optimal for estimating the entire function and are also minimax rate optimal for point estimation. We show that it is impossible to attain the global optimal rate of convergence as well as the local optimal rate at every point. An inequality concerning estimation in a two parameter st...

We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates (n lnn)− s s+d + n for 0 < s ≤ 2 in arbitrary dimension d, where s is the smoothness parameter and n is the number of independent samples. Using a two-stage approximation technique, which first appro...