Recently, Samet et al [24] introduced the concept of α-ψ contractive mappings and studied the existence of fixed points for such mappings. In this article, we prove three fixed point theorems for this class of operators in complete metric spaces. Our results extend the results in [24] and well known fixed point theorems due to Banach, Kannan, Chatterjea, Zamfirescu, Berinde, Suzuki, Ćirić, Niet...

This note considers the problem of stability analysis of discrete–time homogeneous dynamics, i.e., positively homogeneous of the first degree dynamics. An example of a homogeneous and even continuous dynamics that is globally exponentially stable and that does not admit any λ–contractive proper C–set is presented. This motivates us to propose a natural generalization of this concept, namely, (k...

We propose a receding horizon control strategy that readily handles systems that exhibit interval-wise total energy constraints on the input control sequence. The approach is based on a variable optimization horizon length and contractive final state constraint sets. The optimization horizon, which recedes by N steps every N steps, is the key to accommodate the interval-wise total energy constr...

We present a new stabilizing control scheme for linear discrete-time systems with input and state constraints. Essentially, we seek a controller that is able to steer all initial states within a controlled invariant set towards the origin without violating the constraints. The control law builds on a predictive control scheme. We show that a prediction horizon of n steps, where n denotes the di...

A set of np ≥2 -cyclic and either continuous or contractive self-mappings, with at least one of them being contractive, which are defined on a set of subsets of a Banach space, are considered to build a composed self-mapping of interest. The existence and uniqueness of fixed points and the existence of best proximity points, in the case that the subsets do not intersect, of such composed mappin...

Certain discrete-time Markov processes on locally compact metric spaces which arise from graphdirected constructions of fractal sets with place-dependent probabilities are studied. Such systems naturally extend finite Markov chains and inherit some of their properties. It is shown that the Markov operator defined by such a system has a unique invariant probability measure in the irreducible cas...

In this paper, we study for some of the fixed point of mapping for a self map on a metric space under a contractive of integral type.

We present new fixed point theorems for inward and weakly inward Urysohn type maps. Also we discuss Mönch Kakutani and contractive type maps.

In this paper, we prove common fixed point theorems for minimal commuting mappings satisfying (ψ-φ)-contractive conditions in multiplicative metric spaces. AMS Subject Classification: 47H10, 54H25