We consider a generalization of perturbed best response dynamics in population games with continuum strategies. The previous literature has considered the logit dynamic generated through Shannon entropy as deterministic perturbation. wider class perturbations satisfying lower semicontinuity and strong convexity. Apart from entropy, Tsallis Burg are other that satisfy these conditions. thereby g...

In this paper, we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution cone convexity, is straightforward. The results are established under verifiable Slater-type condition, with relaxed monotonicity without lower semicontinuity assumptions the play. versatility of our findings illust...

In this paper, we study the existence of solutions for vector saddle points problems in a general setting. Our approach, first, is based on the KKM lemma and a relaxation of the C− lower semicontinuity notion introduced by T.Tanaka by means of an extension to the vector setting of a Bŕezis-NirenbergStampacchia condition, and arguments from generalized convexity. This leads us to generalize and ...

This paper provides necessary and sufficient conditions for fixed-point theorems, minimax inequalities and some related theorems defined on arbitrary topological spaces that may be discrete, continuum, non-compact or non-convex. We establish a single condition, γ-recursive transfer lower semicontinuity, which fully characterizes the existence of equilibrium of minimax inequality without imposin...

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also i...

In this paper we make a survey of some recent developments of the theory of Sobolev spaces W (X, d,m), 1 < q < ∞, in metric measure spaces (X, d,m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev space based on Γ-convergence; this result extends Cheeger’s work because no Poincaré inequality is needed and the measure-theoretic doubling property is weakene...

This paper summarises the general strategy for time evolving finite elastoplasticity and outlines encountered computational challenges in form of numerical benchmarks. Each time-step of some natural implicit time-discretisation is eventually recast into a possibly non-convex minimisation problem. Finite plasticity seems to imply the lack of lower semicontinuity of the energy functional and so l...