We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it (1) has a product structure, (2) is upper hemi–continuous, (3) always includes a best reply to any mixed strategy profile, and (4) is convexand closed-valued. For each generalized best reply correspondence, we define a generalized best reply dynamics as a differential inclusion...

The purpose of this paper is to introduce a new hybrid projection algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of the variational inequality for an inverse-stronglymonotone operator and the set of fixed points of relatively quasinonexpansive mappings in a Banach space. Then we show a strong convergence theorem. Using this result, we obtai...

In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(ell_{p})$ spaces, $1 < p

We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied to Rényi and Tsallis entropies. The generalized entropy maximization procedure for Rényi entropies results in the exponential stationary distribution asymptot...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of a variational inequality problem for a monotone and Lipschitz continuous mapping. We introduce an extragradient-like iterative algorithm that is based on the extragradient-like a...

We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, som...

Exosystem: A dynamical system modelling the set of all exogenous inputs (command/disturbances) affecting a controlled plant. Internal Model: A model of the exogenous inputs (command/disturbances) affecting a controlled plant, embedded in the interior of the controller. Generalized Tracking Problem: The problem of designing a controller able to asymptotically track/reject any exogenous command/d...