Using a result linking convexity and irreducibility of matrix sets it is shown that the generalized spectral radius of a compact set of matrices is a strictly increasing function of the set in a very natural sense. As an application some consequences of this property in the area of time-varying stability radii are discussed. In particular, using the implicit function theorem sufficient conditio...

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game’s expected payoff fu...

The modification of the Clarke generalized subdiNerentia1 due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The Glteaux differentiability of any real function can be deduced from the GBteaux differentiability of the norm if the function has a directional derivative which attains a constant related...

The main result of this paper is a generalization of the property that, for smooth u, uxy = 0 implies (*) u(x, y) = a(x) + b(y). Any function having generalized unsymmetric mixed partial derivative identically zero is of the form (*). There is a function with generalized symmetric mixed partial derivative identically zero not of the form (*), but (*) does follow here with the additional assumpt...

We show that principles from nonstandard analysis hold to some extent for nonlinear generalized functions. The generalized functions under consideration are constructed as families of functions modulo a free filter, as it is usually done in applied analysis. In contrast with models of nonstandard analysis, we do not require the filter to be an ultrafilter. The principles are intended to be used...

In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem fo...

In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

Abstract We prove local $C^{0,\alpha }$- and $C^{1,\alpha }$-regularity for the solution to an obstacle problem with nonstandard growth. These results cover as special cases standard, variable exponent, double phase, Orlicz

In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem fo...