8 Browder, F. E., "Strongly nonlinear parabolic boundary value problems," Amer. J. Math., in press. 9 Browder, F. E., "Nonlinear elliptic boundary value problems, II," Trans. Amer. Math. Soc., in press. 10 Browder, F. E., "Nonlinear equations of evolution," Ann. of Math., in press. 11 Browder, F. E., "On a theorem of Beurling and Livingston," Canad. J. Math., in press. 12 Browder, F. E., "Multi...

In this paper we survey the relationships between scalar and vector variational inequalities (of differential type) and the underlying optimization problem. We show that the variational inequalities of Stampacchia type can be viewed as necessary optimality conditions, while the variational inequalities of Minty type can be considered as sufficient optimality conditions. Concerning this last sta...

this paper introduces an implicit scheme for a   continuous representation of nonexpansive mappings on a closed convex subset of a hilbert space with respect to a   sequence of invariant means defined on an appropriate space of bounded, continuous real valued functions of the semigroup.   the main result is to    prove the strong convergence of the proposed implicit scheme to the unique solutio...

The equilibrium problem attracted much attention in recent years, since apart from its theoretical interest includes, as particular cases, scalar and vector optimization problems, saddlepoint (minimax) problems, variational inequalities, Nash equilibria problems, complementarity problems, fixed point problems, etc. However, a seemingly interesting special case, where the function involved is re...

In this paper, first a short history of the notion of equilibrium problem in Economics and Nash$acute{'}$ game theory is stated. Also the relationship between equilibrium problem among important mathematical problems like optimization problem, nonlinear programming, variational inequality problem, fixed point problem and complementarity problem is given. The concept of generalized pseudomonoton...

This paper is devoted to the study of a fully discrete T -ψ finite element method based on H-decomposition to solve a nonlinear degenerate transient eddy current problem with ferromagnetic materials. Here, the ferromagnetic properties are linked by a power material law. We first design a nonlinear time-discrete scheme for approximation in suitable function spaces. We show the well-posedness of ...

We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes [17] and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the Klee-Minty cubes leads t o (nearly) quadratic lower bounds for the complexity of linear programming with rando...

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...