We propose a new stability constraint for contractive receding horizon control (RHC), which was inspired by a non-monotone line search rule for optimization algorithms. Previously proposed stability constraints for contractive RHC can be seen as special cases of our new constraint. The new stability constraint guarantees asymptotic stability, but it does not ensure the monotone decrease of the ...

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

Very recently, Agarwal et al. (Fixed Point Theory Appl. 2012:40, 2012) initiated the study of fixed point theorems for mappings satisfying cyclical generalized contractive conditions in complete partial metric spaces. In the present paper, we study some fixed point theorems for a mapping satisfying a cyclical generalized contractive condition based on a pair of altering distance functions in co...

The purpose of this paper is to prove end-point theorems for multivalued mappings satisfying comparatively a more general contractive condition in ordered complete metric spaces. Afterwards, we extend the results of previous sections and prove common end-point results for a pair of T-weakly isotone increasing multivalued mappings in the underlying spaces. Finally, we present common end point fo...

In this paper, we consider, discuss and complement fixed points results for mappings satisfying cyclical contractive conditions established by W. A. Kirk et al. [W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, Volume 4, No. 1, 2003, 79-89]. By using our new Lemma we get much shorter and nicer proofs of some re...

‎in this paper we study the existence of fixed points for mappings defined on complete metric spaces‎, ‎satisfying a general contractive inequality depending on two additional mappings‎.

This paper presents a stabilizing tube-based MPC synthesis for LPV systems. We employ terminal constraint sets which are required to be controlled periodically λ-contractive. Periodically (or finite-step) contractive sets are easier to compute and can be of lower complexity than “true” contractive ones, lowering the required computational effort both off-line and on-line. Under certain assumpti...

We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable periodic solution. Obtaining explicit information on this periodic solution and its dependence on various parameters is important both theoretically and in nu...

*Correspondence: [email protected] Mathematics and Computer Science Department, Çankaya University, Eskişehir Yolu, Yenimahalle, Ankara, 06810, Turkey Abstract Recently, some authors have started to generalize fixed point theorems for contractive mappings in a class of generalized metric spaces in which the self-distance need not be zero. These spaces, partial metric spaces, were firs...

An analysis is given of ∗-representations of rank 2 single vertex graphs. We develop dilation theory for the nonselfadjoint algebras Aθ and Au which are associated with the commutation relation permutation θ of a 2 graph and, more generally, with commutation relations determined by a unitary matrix u in Mm(C)⊗Mn(C). We show that a defect free row contractive representation has a unique minimal ...