Variational inequalities theory has been widely used in many fields, such as economics, physics, engineering, optimization and control, transportation [1, 4]. Like convexity to mathematical programming problem (MP), monotonicity plays an important role in solving variational inequality (VI). To investigate the variational inequality, many kinds of monotone mappings have been introduced in the l...

Complex economic models often lack the structure for the application of standard techniques in monotone comparative statics. Generalized monotonicity analysis (GMA) extends the available methods in several directions. First, it provides a way of finding parameter moves that yield monotonicity of model solutions. Second, it allows studying the monotonicity of functions or subsets of variables. T...

We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non-decreasing operators,...

This article studies the monotonicity behavior of plural determiners that quantify over collections. Following previous work, we describe the collective interpretation of determiners such as all, some and most using generalized quantifiers of a higher type that are obtained systematically by applying a type shifting operator to the standard meanings of determiners in Generalized Quantifier Theo...