The purpose of this paper is to construct two superimposed optimization methods for solving the mixed equilibrium problem and variational inclusion. We show that the proposed superimposed methods converge strongly to a solution of some optimization problem. Note that our methods do not involve...

In this paper, for a monotone operator T, we shall show strong convergence of the regularization method for Rockafellar’s proximal point algorithm under more relaxed conditions on the sequences {r <Subscript> k </Subscript>} and {t <Subscript> k </Subscript>}, <Equation ID="Equa"> <EquationSource Format="TEX">$$\lim\limits_{k\to\infty}t_k=0;\quad...</equationsource></equation></subscript></subscript>

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator...

We study increasing quasiconcave functions which are co-radiant. Such functions have frequently been employed in microeconomic analysis. The study is carried out in the contemporary framework of abstract convexity and abstract concavity. Various properties of these functions are derived. In...