An Iteration Scheme for Contraction Mappings with an Application to Synchronization of Discrete Logistic Maps

This paper deals with designing a new iteration scheme associated with a given scheme for contraction mappings. This new scheme has a similar structure to that of the given scheme, in which those two iterative schemes converge to the same fixed point of the given contraction mapping. The positive influence of feedback parameters on the convergence rate of this new scheme is investigated. Moreover, the derived convergence and comparison results can be extended to nonexpansive mappings. As an application, the derived results are utilized to study the synchronization of logistic maps. Two illustrated examples are used to reveal the effectiveness of our results

An extragradient-type method for generalized equilibrium problems involving strictly pseudocontractive mappings

Strictly pseudocontractive mapping, Nonexpansive mapping, Inverse-strongly monotone mapping, Equilibrium problem, Variational inequality, 47H05, 47H09, 47J25,