Showing papers by "Manuel De la Sen published in 2014"

Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces

Abstract: In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.

Pata contractions and coupled type fixed points

Abstract: A new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

Abstract: This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical identification of dynamic systems.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Abstract: Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed. MSC: 47H10; 54H25

Properties of convergence of a class of iterative processes generated by sequences of self-mappings with applications to switched dynamic systems

Abstract: This article investigates the convergence properties of iterative processes involving sequences of self-mappings of metric or Banach spaces. Such sequences are built from a set of primary self-mappings which are either expansive or non-expansive self-mappings and some of the non-expansive ones can be contractive including the case of strict contractions. The sequences are built subject to switching laws which select each active self-mapping on a certain activation interval in such a way that essential properties of boundedness and convergence of distances and iterated sequences are guaranteed. Applications to the important problem of stability of dynamic switched systems are also given.

Adaptive control of SEIR discrete-time epidemic models

Abstract: This paper applies the Micken's discretization method to obtain a discrete-time SEIR epidemic model. The positivity of the model along with the existence and stability of equilibrium points are discussed for the discrete-time case. Afterwards, an adaptive controller is designed for this system ensuring the non-negativity of the estimated parameters and the convergence of the exposed and infectious to zero eradicating the illness from the population.

A nonlinear SEIR epidemic model with feedback vaccination control

Abstract: A mathematical model describing a generic disease is introduced and the dynamics of the subpopulations are studied. Through linearization of the continuous-time model, the stability of the equilibrium points and the characteristics of the disease are defined properly. Due to the nature of the disease, the model is discretized in order to apply some adaptive vaccination strategies involving feedback loops. Furthermore, such techniques are compared to the traditional regular-vaccination strategies. The obtained results indicate a possible improvement in the use of the adaptive strategies for vaccination.

Event-based generation of approximate solutions of nonlinear differential equations

Abstract: This paper investigates the error between the approximate and exact solutions of a class of nonlinear differential equations which possess unique solution on a certain interval for any admissible initial conditions The differential equations are assumed to be approximated by well-posed truncated Taylor series up to a certain order obtained about certain, in general non-periodic, sampling points t i ∊ [t 0 , t J ] for i = 0,1,…, J of the solution Two simulation examples are also provided The first one is concerned with a predefined periodic sampling law while the second one generates new sampling points according to a constant amplitude difference sampling criterion