The Independence of p of the Lipscomb's L(A) Space Fractalized in l^{p}(A)

In one of our previous papers we proved that, for an infinite set A and p\in[1,\infty), the embedded version of the Lipscomb's space L(A) in l^{p}(A), p\in[1,\infty), with the metric induced from l^{p}(A), denoted by {\omega}_{p}^{A}, is the attractor of an infinite iterated function system comprising affine transformations of l^{p}(A). In the present paper we point out that {\omega}_{p}^{A}={\omega}_{q}^{A}, for all p,q\in[1,\infty) and, by providing a complete description of the convergent sequences from {\omega}_{p}^{A}, we prove that the topological structure of {\omega}_{p}^{A} is independent of p

New fixed point theorems for set-valued contractions in b-metric spaces

In this paper we indicate a way to generalize a series of fixed point results in the framework of b-metric spaces and we exemplify it by extending Nadler's contraction principle for set-valued functions (see Multi-valued contraction mappings, Pac. J. Math., 30 (1969), 475-488) and a fixed point theorem for set-valued quasi-contractions functions due to H. Aydi, M.F. Bota, E. Karapinar and S. Mitrovic (see A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88)

Polling-systems-based Autonomous Vehicle Coordination in Traffic Intersections with No Traffic Signals

The rapid development of autonomous vehicles spurred a careful investigation of the potential benefits of all-autonomous transportation networks. Most studies conclude that autonomous systems can enable drastic improvements in performance. A widely studied concept is all-autonomous, collision-free intersections, where vehicles arriving in a traffic intersection with no traffic light adjust their speeds to cross safely through the intersection as quickly as possible. In this paper, we propose a coordination control algorithm for this problem, assuming stochastic models for the arrival times of the vehicles. The proposed algorithm provides provable guarantees on safety and performance. More precisely, it is shown that no collisions occur surely, and moreover a rigorous upper bound is provided for the expected wait time. The algorithm is also demonstrated in simulations. The proposed algorithms are inspired by polling systems. In fact, the problem studied in this paper leads to a new polling system where customers are subject to differential constraints, which may be interesting in its own right

A characterization of compact operators via the non-connectedness of the attractors of a family of IFSs

In this paper we present a result which establishes a connection between the theory of compact operators and the theory of iterated function systems. For a Banach space X, S and T bounded linear operators from X to X such that \parallel S \parallel, \parallel T \parallel <1 and w \in X, let us consider the IFS S_{w}=(X,f_1,f_2), where f_1,f_2:X \rightarrow X are given by f_1(x)=S(x) and f_2(x)=T(x)+w, for all x \in X. On one hand we prove that if the operator S is compact, then there exists a family (K_{n})_{n \in N} of compact subsets of X such that A_{S_{w}} is not connected, for all w \in H- \cup K_{n}. One the other hand we prove that if H is an infinite dimensional Hilbert space, then a bounded linear operator S:H \rightarrow H having the property that \parallel S \parallel <1 is compact provided that for every bounded linear operator T:H\rightarrow H such that \parallel T \parallel <1 there exists a sequence (K_{T,n})_{n} of compact subsets of H such that A_{S_{w}} is not connected for all w \in H- \cup K_{T,n}. Consequently, given an infinite dimensional Hilbert space H, there exists a complete characterization of the compactness of an operator S:H \rightarrow H by means of the non-connectedness of the attractors of a family of IFSs related to the given operator.Comment: 12 page

A generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions

In this paper we obtain a generalization of Matkowski's fixed point theorem and Istratescu's fixed point theorem concerning convex contractions in the framework of b-metric spaces. By providing appropriate examples we show that the above mentioned two generalizations are effective

A generalization of Istratescu's fixed point theorem for convex contractions

In this paper we prove a generalization of Istr\u{a}\c{t}escu's theorem for convex contractions. More precisely, we introduce the concept of iterated function system consisting of convex contractions and prove the existence and uniqueness of the attractor of such a system. In addition we study the properties of the canonical projection from the code space into the attractor of an iterated function system consisting of convex contractions

Caristi-Kirk type and Boyd&Wong-Browder-Matkowski-Rus type fixed point results in b-metric spaces

In this paper, based on a lemma giving a sufficient condition for a sequence with elements from a b-metric space to be Cauchy, we obtain Caristi-Kirk type and Boyd&Wong-Browder-Matkowski-Rus type fixed point results in the framework of b-metric spaces. In addition, we extend Theorems 1,2 and 3 from [M. Bota,V. Ilea, E. Karapinar, O. Mlesnite, On alpha-star-phi-contractive multi-valued operators in b-metric spaces and applications, Applied Mathematics & Information Sciences, 9 (2015), 2611-2620]

Iterated function systems consisting of phi-max-contractions have attractor

We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image turns out to be the attractor of the system. Moreover, we prove that the unique fixed point of the operator associated to an iterated function system consisting of convex contractions is the canonical projection from the shift space on the attractor of the system

Invariant measures of Markov operators associated to iterated function systems consisting of phi-max-contractions with probabilities

We prove that the Markov operator associated to an iterated function system consisting of phi-max-contractions with probabilities has a unique invariant measure whose support is the attractor of the system

A new algorithm that generates the image of the attractor of a generalized iterated function system

We provide a new algorithm (called the grid algorithm) designed to generate the image of the attractor of a generalized iterated function system on a finite dimensional space and we compare it with the deterministic algorithm regarding generalized iterated function systems presented by P. Jaros, L. Maslanka and F. Strobin in [Algorithms generating images of attractors of generalized iterated function systems, Numer. Algorithms, 73 (2016), 477-499]